Question
![2000 minus 61 k equals 48](data:image/png;base64,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)
In 1962, the population of a bird species was 2,000. The population k years after 1962 were 48, and k satisfies the equation above. Which of the following is the best interpretation of the number 61 in this
context?
- The population k years after 1962
- The value of k when the population was 48
- The difference between the population in 1962 and the population k years after 1962
- The average decrease in the population per year from 1962 to k years after 1962
Hint:
Hint:
We need to understand every term in the equation given. We are given the number of bird species in a year 1962 and the number of
birds after k years. So, we are given that the relation between the years passed and the number of birds species satisfy the equation.
The correct answer is: The average decrease in the population per year from 1962 to k years after 1962
The given equation is
![2000 minus 61 k equals 48](data:image/png;base64,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)
Given,
Number of bird species in year 1962 = 2000
Number of bird species in year 1962+k = 48
Solving the above equation for k, we get;
Also, k satisfies the above equation.
![2000 minus 61 k equals 48](data:image/png;base64,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)
![61 k equals 2000 minus 48](data:image/png;base64,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)
![61 k equals 1952](data:image/png;base64,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)
![k equals 32](data:image/png;base64,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)
Thus, the population of the bird species in the year (1962+32=)1994 is given by 48.
Rearranging the equation
, we get
![61 k equals 2000 minus 48](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHwAAAANCAYAAABrYAraAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAr1JREFUeNrtWFGEVFEYvsZYV1bsQ7J6WLJW1lqRJCMZspJkLcnax0iS9NZD0lP00EP2IZKxksTKSJLIWCPJkJUeVmKfkuxLD2uscS3Td/gmd/49587t7n9OD/XxcefMP3fu+b//fOc/N4r6cRRcBjfBDvgSPBntxAR4C/wUZWMLLEV+UQGf85kTPtOCI3Yv+ABskQ855jtOG2fBruO7PeAi2KaGb8ADtsBLFHgiNRmTuHeW2CeM72Y81Dj4OcDkm+A8OMzPk+B7jkk0wHMicY0AcZow81zLyH0NvAOWwSHwLouxDyZJHwv8eZbgs+Cz6O9gzFJs51n5EvdFcWjHacO4yMWM3HfE5xKdb8dN5pUFvw3e4LWptsfgmYCiy4kb25+xxFX5na847e2rMSD37ZTb9QT/JoO+gKPKgi9zlce8rua41yDmxXHaeho/aXESZmzDY5wWhuhaYwNyb1znmsjFPdtqMHt3nY1WQotf2IXgX8Ep9gXHAq7smHtWRYxvZ/wm8RinBbMXX82R+2n+f8L+5gd4wibcKi23TBuoULQrBQQvsXA+UPRQGAFfOKx2O6f9a8dpuNi0xbG6jt7lKd265z5HwHXe4zc2Ha37YfB7AcHNil5hX1D7g+1hN5Z+kGKPO77fcFhwLCxYO04DLcu8bPmoS2FTfcVKeuB1xnk5KSC4EXqJ12b/uOx5ZR8CH/EM6oJppE5bxmcszZhmnAbyLoROXtcxtn3BkchWAcEXeU7v4a1lT9XCfjaF5QFxcywKiSVxQtGO8wVb7tccDjfJvbyvA2zyfFdO2bLpCk8VELwujmAjLJxRDxN/xcLMA2Nr11MvJW5y3r7jQgk+R9GrdOwSr9dtLruPFdtmQ9K0dXcZFiOPQLEYm+IZMg5od7amrkZ72+L7h+EAcaEE770QWuVW3KGOs9F//Jv4Bf5o+SzisPo7AAAAh3RFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtbj42MTwvbW4+PG1pPms8L21pPjxtbz49PC9tbz48bW4+MjAwMDwvbW4+PG1vPiYjeDIyMTI7PC9tbz48bW4+NDg8L21uPjwvbWF0aD744VT8AAAAAElFTkSuQmCC)
![61 equals fraction numerator 2000 minus 48 over denominator k end fraction](data:image/png;base64,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)
Clearly, the right hand side of the above equation gives the average decrease in population from 2000 to 48, in k=32 years.
In other words,
61 denotes the average decrease in population per year from 1962 to k years after 1962.
The correct option is D)
.
Note:
This question could also be solved by eliminating the options. Option A is wrong as the population k years after 1962 is 48, not 61. Option B is wrong because we find the value of k to be 32. Option C is wrong because the difference between the population in 1962 and the population k years after 1962 is given by 2000-48=1952.
Related Questions to study
The figure on the left above shows a wheel with a mark on its rim. The wheel is rolling on the ground at a constant rate along a level straight path from a starting point to an ending point. The graph of y= d(t) on the right could represent which of the following as a function of time from when the wheel began to roll?
The figure on the left above shows a wheel with a mark on its rim. The wheel is rolling on the ground at a constant rate along a level straight path from a starting point to an ending point. The graph of y= d(t) on the right could represent which of the following as a function of time from when the wheel began to roll?
Which of the following is equivalent to
?
Which of the following is equivalent to
?
![](data:image/png;base64,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)
One method of calculating the approximate age, in years, of a tree of a particular species is to multiply the diameter of the tree, in inches, by a constant called the growth factor for that species. The table above gives the growth factors for eight species of trees.
If a white birch tree and a pin oak tree each now have a diameter of 1 foot, which of the following will be closest to the difference, in inches, of their diameters 10 years from now? (1 foot = 12 inches)
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RL3EiGBrWz4r9fUNDZQVW5nrSb7+HaeN8zWgqP0ARCxXLWrNtLo76FI/sP4zn+Pn52Ywqm7G/46MtVHC5vwqGNYEhCCCrZd09Z4ahj8+LF7MlpRiVrZ8+mdezMKcEo9yM5IQpPtQyPkFg8O3NZMu9zlq3aRKHejbSJ1zIxLYSaPUv55IulbNqZDaFpjBoUgfoi/XB7GgwAmZa44WOIFE+wfsUassqbaGuqJnvvOr7ZUojPsKlMSlCwYf48NmQW0YEn8fEx+GrlqP1iifNqZcu6rZS1dFB4YC/mhFt55I5x3cYMFYKpngaHDzfeOAVfNw2O5hrMniO44drYLsupSqApdxvLlm2lSm+n9vgutu7IpNHiRcrICPJXfcrKrdm0OPwZPG4wPoquZ2oo28/n8xexO78Sk9yf1KRo/H3kHN/xNV9vyqBJ44Gt5AAHahRcN+tWApt389m8hazdvI8mZTgjR6birVHg0GWzctFKDpebCB4zneuTZOzdsJHchk4qDu2gzn8aj//8erx1R5g/bwHbc8ownKwzzZkV0BeDgXD2HgbPP/Msb/79rYv3bZPs6JtrqThRh901gMiIUDxd5AjY2PX2L3inZAh/+vPdxGvdcffUntH42IwtVFXUIXqFEhbgwcn3VHLaaKstp9bkQkR4IK5KsJgt2J0giHJUKhUyEeymVipP1CB4hhIW6IlccNDZVEt1YyfagDBCfF1772IlB8a2BmoaDLgFhuDn4dLVAtosmK32rtZTpkSjUiCc3kJJdhorStALPoQGeSDZ7V3jbVGOWqVEdnJhQ7LTWlNGjUFFREQwrmoFAuCw6Kk+UYFNG0JEsBeKviyEnEVhQQGrVq7kpZdf7uVbJxajAX1LA9V1LaD2IjA0CF83DXJRwmK2dA97ZKjUKuSn5HVi6Wimuq4NtU8Q/t5uJ1cDuurJoKfNbMfDxxslEobOFsxWNT7e370rto4Gyqr1+ISE4Kqga8FUkKFSK3FazdgcEoIgQ6VWnxoySQ4rZouta9QnylGrVcgEMLVUU9PiwDcsFFVHHTqnF0F+WkSnmaaqclokbyJCfdGcHI3YOqk6UQ3ugQT5e6IQJGydLdTU6hDd/Qn080QpA5x2TGYLTgk4u866OXr0KHt27eLZ558/Zx30n3uOIMfdL5xUv/CzvpAhE0TkWh8iQ4Lw6uVUhYs30UnePS8pKvAKjT/jHJVG3sNlQ67xIjrp9FIyXP3CSPS7kMwyXLyCiTtLKFGhwkVxngmkIMc/MhH/k8fn6qUFeQ/5AWQqdyISUi8g3A9BROXihp+LG369rDaqXc5R7YKIyt2fGHf/Xr9WaN3xO6UnAlpXH85uYhVuASQkncNypXahtyclyJRoXHp+o/EOJfbka6EK/W7hVKbGPzKJs6UUFK6Ex53uQiWgcPUhMv6sJVNRjuZcz+AiuOSOoZ1VOWTml1FffITMwibsV6RPy9WJ8EMG7AOcF3kf4tl6qJ/FYmHRwoWo1T/cqUYQJNpqSigRw0jw0bNj0Vxqo4JQy78zSQ5w8YgyGXU1NeTl5fLVkiVYrQM+3/2JIAhUVVVdcN7fa98ldP/5wUgCnsEJjA1LRsSJw+nsUpoe5swBLgbxVP0I/VdXA5xCQEA45xrfd/RQHpVKxX0/u38gGO4Kp7CgALvdzt333nO5RflJciwnh507dpy3zI8eDGdsraWssgn7j31jAJuB+hOVtJgvy937HanPIWYDXCyOPuwNcUGTg72pmP055VgcAgggylV4+oeTkBDJxTkDmynavpj33l9My5Cnmffqbf0ciXd+7O2lLH33Nb444MFv5r7F9cE/5t3/93BaLdhFFcpzPGbJYe8yYwMgIMrlfQpduJK4YM8j06ixVO7m7Zf+wrqcZmT2Rtb+6zke/tX7HGu+mC2q1CRMnc11KSqaWzt+9DZT7hHD1GtGo7C0orcOmPwuJc6Ww/z7hSdYknMOQ4b1KO88di933H4ns++8nTvu/i3rijt+XCH7gQs2v4JrGGOnTCB0eRbxwycweXIYwyMVPPGzN1iwZSJv3DuUvnvTu+Hj6Yqiv8NL+4iruxsu3QuVA1wiHDp2rljA6vQaHnqs9yftbKyiNWAyLzyShkJygsqXlMirb47dt7GL1OXPd3KMrfaMIMhbxG53fteD2PUUHzlIZn4dngkTmDom+tRipt1Ux5E96Rxv7CQ/uw5HwNk2dCedDaUcyTqOIm4Ifm257D+mI2rstYxJcKFw9zayTthInjiV4TE+iIDT3Ebu/m1kVTgZfO1NDA93xaqvIyczg5JGLcMnh1K28yDNinAmTJtEhLusp3ncouPYoYPklLYSPGQyE9NCftSh5E8PG4W791AlehLqrjnneoS1vhHt4ClMmZj8I8vXv/TdYCBxaoO9sowtNHhN4OYJyV0rxvYO9q/+il0nVKQmurPtP3/k460VADjqD/HJ2/M44RLH8HgfHCYrvW2M0l6yj3n//BtvvzuX3cebaCz8lrf++Dvefn8px2paKd+/gNfemkdRKzgbM/j4nXc5bPRGVr6O1974gnIniHYjxTsW84+332XxukwaW2vY/PGfee7leVTCqTG1IMrA2sSmpcvJ0fuSEmZn+T/+j68ONfUUbIA+016STnqpnZGj03BTnNuc0dbYSkPBOt58+Tf8+qW3WXOw8vIYkH4gfVIeQZAht7VxZPMy/vnHx3jxwxPc9/pfmBrV5Wuvy9vA8rVH0AT4o/EIJcRFT8bebNppZ82cd8jxuoZbJ6SSOGo6144IRSGcrT0iIakjSQnxIyRlKvfc/zOefuI+QoxN2OPGc9f9D/PUL+5EVZ9JQU0rZqMBhd9Qpk2fws2TU7HkHSKvVkLuHcPEUUm4+yYw9a57eODJP/LW72+hc9+XrNxvQN7tNCcX7VTuX8G6fRW4+Xqh9YnA11HLgYx8DP36eP93kIy17N2XR8iYm0gOVoFTQJT3vsiojL2G22+YzPRbbyDGcZQ3n3mOLw81/8gS/3D6NEqRJAd2pRdpk6czQ6lg25YVZByu4KaYZAQk6rL2caTGSkRFDkeblCTM/gPTEofgVn2ADfvqifh9UrdPk4BwLnWVK1Aqlag0GhSAXOuOh1aLXKlABri4+eCuFjFa7LgMmsI9txaS+e0aqvMrceLE2R3goZDJkckVqNVdPy147BgGu6+mrbUTXLsXFm1Gyg9lUtigJaX4KHaNinGPvUJUYhKac4g3wPlwkrvhU77eBzcFHmTjkQzqO1vI3bGBHLfhJEUHnDEv9o4fyeT4rv8PSfKl8fgTbPw2l5+PnNxbtMIVS5+U52SAkULjQdzkp3j+toP85ZP/MGbYP7gxRotkt+B0DWT89LsYeboP3gk7doeR+roG6N7PRKTL5N1jKnkqilD67oNeEGUChuJ1/O2dzQTd9Ai3XzOcjRt3nxpe9zirQ49ZE82EpAAk/Xc9ntNuAu80rps1m7irb656xaENGcYNUw3YdY206I3YnA6Mne0YTBfY8NDNHW+PYCJDvK+6HTj7JK/NasDYYaLTaAZUTH30V1yjPsjbf5/L8Q4nEZOmEtqwkf/8dxmlTS2UHN7B1gPlSJHDuHaYLwcXvcfa/GbsplqqalsxtrbTdvYg127DajVhsnQFzTntNixmMxZrV0GbzYzZZMbqcNJauI/tOTrCB6eitbTT2tFEc3PXjmSCIOC0dtLR7gCnnn1rD+B1y8+5MRpMJgsWkwkzKuInjkdzbDFz5m2ipqWZY/u3sSe7qsdeBwP0BZHosTO5+557uPe+e7h/5hj81G4MveEuxqaEonTq2D7/PT7fmI8dPYe/3cDB4hZAoj79ILr4m3loZvJVZwW9YDCcvSKd+QtXkVfWSmenEZeIVOKjYkkbHELD/g3sKHQwYsYsRgVZ2LNyIQuWruOEI5xrrx+Hn4sHyamxdORtYuHCNRyulnChhbp6HXZNGImJQV0WObuBzHWLWJdRRKtJRdTgBMq3LmRHTgUdZhciB/mS881SDhY0YsCb4dePQcjbzNLVu2jzj8W7NZ+sShvJI0fgXr+PL1dtIS+3gKK8Ukiczi/uGYeyvYRvli4lu7yJDqsrI264nWFezWxe+iWLvt6Czi2Fa6eMwFt1dVRhr8FwVwAtJftZ8PlSsmraaWnV4xcZT7hvK6v/9T4Z1niunxTG8bWf8fb7X7D7aCHNyjjuvH8WCd4XE3x56elLMBzSWTz39DNSZ2fn2R+fA4fU2domGe1OSZIkyW5sl5pbOyWH88xSTrtV0re0SWaHJJkNBsnudPZyrYvDZuqU2ts7JLskSU5Lp2SwdH1et/516bqbfift0bVJRqP9wtfpbJWa2kw/WJ4fm4L8fOnNv/71covRZ+zGdqnDcvLIKXU2N0i6DtvlFOm8HDlyRHr/3XfPW+YHLmuIaD2/2+tKpnHHp5cZtyBT4ObVXc6lH3aKAeRqLe4noyaUWk5eVRREJElA5eGBpg+zT7nWE99+kWiA8yHTuHdtEgKAgNbHv0cg3dXG1TZHOy/GpmK27jtCS91Rtq7eT0PHgOPkAN+Pvgzee/Q8VouFr5evQKO5uoy2ggjm9iZqlMnccouEoyiddR2VeLqIOH9iOiSTyaiuruZ40XHWrF6D1dI/u+8M0IUgCFRUVFywXA/lcUgSra0tmEz9uT37j4UMr4AQvAVAkrCbWmn+CSZNE0WR9vY2TCYTLbrmgUjSfkYQBPT6dtzc3M5brofyuGg0PPb44wPBcFc4hQUFKOSrePjRRy+3KD9J8vPy2L5t23nL9JjzSD2c+c7cPvXyIGHR15KTnU9TR3+2sk4MzRVkZ+WfuSniVcJAMNylw2qz/fDMcLaGfL7dfZRGvRWl1hWtRolS40vi8GFE+Wi6JlZOI0UH91GvSWDskPBetxf6ITgNpSz+y6+ZcyyIf374NlPczrqDZKEscw/lRDF+ZEyf8wF1VGTwn1dfYk3DeD5a/Ve8rybfkCsQyW5BV11OdbuEX2g4wT7ac0y8bbQ1NNJ+KqJXgWdgAB6qq6sCLmhtU3gG4CNUsOg/n3C4RUNUqDslG//Fk0+9zu7ybjdKawdHNixl9e4ijJcgzkzUxjLjvtuJcTNh6c391m4i99tlrNyWi/4i3HPdIsZw78wJuMjsPzmjwo+Oo5PcrYv44D9z+PvLT/LgY39i4/HO3ssaD/Pv557ihede4MXnn+NXv/0X+6qvvsnphdd5VL6kjh5BROheYpLTSBseRlwgZM/+Dat2z2Js1CiUaj9mvfRvbkaF6yUyfguSiCgTkPXWlik8uOHFfzLFqcTtIleuBFFEPMfm4wP0HZu5kw4xlAdfeYRwy35+87NnWb29kOnxI3qUtTfU4hx0N2/cPRIFTiSFO2HhV98cu29e1XbnGVkOZHJXXN3VaFQq5IClroCtWw9gDBzFjeM8SV+2juPtFrQRI5g5LZWqHSvZW9KOb/IUZl6bhq10N+u2ZtFEANPumMXgQBfayjPZsiULZdpY3Et3kWNN4K57ryfoZESdICBIZo6nr6VkZRF671Rm3jqD5EAN1sbjbN+6nzaPFG68YRTu+mK2btpLi2cMUco69mWbuOHhhxjkbaQsfSvrtx2kWRHNzfffS6BChiiYacrbxqeb9tKoTWb2A7OI97rIbFP/48hd/Bl17fXIZeBocuIaOprRo6J7LWura0QVM4Gk+Lirus3qYz8hIDjtGNpb6DQ0c2jTOozxt3HXtSmIgF1fza4VC1i1pxi7Noyhg1zYtXQ5JWZXfF09CA2WU57bRHhaCpasRcxZ28jk+x5gkGkH//fKJ5SbndiaClm/dDGLPp/Plpxyqsoq0Z9uGxBEMLTSKnkxaEgcjVve57nfv8sxnYTM0kj66gUs316ASQDB2MihjV8x7+P5rD9wjPLSCpp1NWyb/ynbqty5/vabiVA0UFzehEMUsTQVknmsk9ihMTRtm8NrH+8YSB1/kQiCiBwjx/cu5eXn/kZF4GiGRnj0Wra13YwufyUvP/coD/z8GeaszIRXM/MAACAASURBVKTzKjTY9C0kQRCQOQyUHNrOJ3sPsjrTjZfmf8hQv67TtXGjuGZoJMtsXSks/IfdzOxJa1mWmUPT7CG0NzQRftPDTAg4wbsvLad1yIOcyCvC6h6MS0c9VSaRSYPHMCJyAdt9JvKH12/D/Wy1djqQXIMYNX4CE+PdSAlV8PTj77Nk1yzevH0M146Mobimy/4khg5j8tAAth+IZPZTrzDYG0o3vc+cPIEn/zyZBFdISB4LQMVqGwrfFG6651aGKcG1Yhe/3X2YOtv1RAx0PheFw6inw+HO2FkzWT/vA379Fxtz3n6MqLMsOK6Db+SRSBmeGitH13zM3//yW0xuX/K7aWGXR/DvSZ96HklyYld4MnjyTB548FbC7MfYuOEgpjPKgCB0x+TIfBh9/XjsBbvJOJ5HVq6TkdNioTSXQ2VW1C4ynHYHfkNn8ec3X2CUF+B04sCD6JhwNOeRytltPvQOSSYpVE1dbdupBG7fZTKQsDs1BIVE4OMJ0ElpxmHq8MPDtdfLnhqTumjdkDnsWAYMCBeNzC2Q4dfcxK13/5I/PjkFY85OCqp7lnMPSSA1KZawyGRmPvUEtyRaOHTg+FUXDtK3MGxRQEBClKvwS72XFx4cyqEv32dlVuOZZYTvNn6NHDqZoR4NrJn/OcW+UxjtAchVqAQ9DvcUJk+exJiRQ0mMCuw2LQsIQnfSpXPIIUndwXSA09iJHk/iYvwQkBAEgdPDVEWhO82eBCBDqTRTU5pHbdOZV+86TzileIIgIIg/LGPYAKBQuuHpG0XAhTJVyEXkqnBSk8KuqihS6IvyOIw01FbRUKejurqWTmDEPb/inqQ6PvjrP9le0obT0EpjUyONTQ3o2rvP807h+kkhHPm2jMRJyV1huJGjuPWaIHa++3veW7mHoxlbWLR0K3UWkNp0NOmaaWyoo6Wzp71bkMlwNteQU1KBvqOZjH17ccZP5Y7xsWBuor6xkaamenRtgKmdhqYmmnUNNDbbAQ2DbrqV6MYNvP7G++zMymbHmhWs3XmUCl0rHbommnRGJCw0NjbR1txEQ4tpYAnyIuis2MXcOV+SXlRDY/UxdmVbmPXiLxnuAThqWfra87w2/wBWWti18FOWbs2mtrGeYxv3YR13D49O7+80k5eeCwfD1R5j4/YsDLiiEiVcAuOIDA4hZXgqmsZ8ssvNuMibyStvQaaQ4RoQQ0KoOwIyfF0FjEHDuG1iEi5yAXAhLm0wboZidmz8liPVMsbePIPBAXKKD+0iu96EXHSi9IkgPsT9DEuMqJDjaKkgN6+Uuro62pVR3PnA3cR7ymjO28eu/AZkSjla/0j8DYXsyatDphRB409iTAAeQfEMivKgMmsHm3dlI4say4RkLYWHc7Eq1Lh6huCrbuJIZgmSXIWLVxixMf79vuDbX1xpwXCOzlr2rF/Jhj1HqWmTSL7pZ9wyrDtPrKQja/MOGlxTmDAiBN2xXSxb9g1HShsQQkYwe9ZUAl2urK7+RwiGkyS7ySTZzhXc5rRJVptD6vmtQ7LbLZL1e8TEmTv1UofZcfEnnpLJKpntPzwY73JzRQbD2W2SxWyRenu8TqddOj000WkxSqYrNxbuxwiGA9n58vgIchS93kFEJlN+rzGuSuvWIzPcRSEouMq8QK4eZPKutIW9IAiyM+pbUGr67EZ1pXJl9ZUDXBQDeXkuHTLxwqrRa2a4rxYtRq252tuFny4ymYyamhry8/NZvnTpQDxPPyMIAlWVVcjl5x+Y9fhWkiRMZtOAu/sVjCiKXVnB7TZMJtOA8vQzgiBgtpjRys/vb9dDeTQaDQ8/+uhAMNwVTmFBATKZjAcfeuhyi/KTpLCggK1btpy3TB+C4QboiYSjt93qf2Sc0uWX4aeK2WL54cFwZ+Kgo7WZ5sZmOq3g4uFLgL8vrur/FfOVlYbCTLbtPIQ5bAoPzhg8kJLkf5g+172puYjNa7bTILji7+MBhmaKsg/TEHQTf3l2Bu7/E/rjxGRoYu/KuVSPi+XBGYMvt0BXFMbGAr5d9Q1Z1TZiR9/IzBtG4N2rc62N8vRNpBe34xQ1xI+byshor6vOdtgnU7Wl/iBzXn2NXTofJk6bzo3TZzLr7p/x89mjMRXmU9V5ofBNO5UHtrBhd053Cg87VQe2sn5X9lWW0kNN5PBbmTY8GKX8aqvqS4u9vYS1C5ZRhh+Bimq+fOOPfLAmv1dnT13GIt6cdwCPwSOJFo/zwb8+47DO9qPL/EPpQ8/TwaYP/s6WtpG8++ZdJLuf/FxJ0IjZPN15CI385NjQgaG9HYPZjlLrjrurGhFw6EpYNfcjcuIeJHV4AjLTCVbP+5AjMQ+QOiwBpVaFQhQAB0a9nk6TFYXWHQ9XDSIgOe2YTWYkuRKFZEWvNyHXuuOuVWLp0GN2dq15yFUuaNVyHA4nMpmAxdiJyWJHQobG3R21zIGxQ4/BaEXm4oanm8tprYeE1dSJvsMIChc8vdzOeDiSw46hvRWT00qLycZVv91lP2NobSZw4sPcMSocObfj3ngnCzbtoebOZMLPKFnPxoXLMUS8wE1DEhCjrmXD0v9jxdZZDL/76vJvu6DyOBoPsHpbFfEP/e40xTmJmtTJE7v+6zRSsHsjO3ObUQid1DU7GHzjvcwcHcaJwzs5fKKeBvMuVn0FKb41HK6op864i5VLRabfezPxWgvH92xke3YDctFEXaOFlOvv4ZZxkdhrMvj43fmUug5iYpIr2Tu2USlP4Ze/+yUhNVv4aO5qmn3G8PAvH2Z8aD3L5+Ux/vGZyEt2MvfDtXTGXsfjj9+GmLeJzZk1yGRm6hsMxE25m9uuiUWJhO74PtZvy8Ysiujr69Akz+D+20bjKQfJ2kzW1m3k17fTWneC3Vk6xBsH1pdPxyNyDNdEnjxyxdfPE027Oz02V24oJrNIT+i42K6GyyOU6GCJlYdzsN4dd8X6EvbGBd8AS3UplQYFfn6+5x2T1mV8xT8+3k7IlHt47OnnuSGymY/feJvtlWZixt/E6OggIkfdzEOP3sq1U6YzKiqIiFE38/BjtxCvFWnMWs4//rsZvwl38dhTz3Nzgp65b77FllIDag9f1KYaCgobcE2YwhPPP0JA9VYWbywgZNwsxvh0UtXuQlS0O+3pa/nkk4/ZeNRGUGoMbh7hTJ11A95V3/D2e6txHXk7jz35ArelOVj41pusL9AjdR7jo7+9S7nHBB574kl+cXsy6R/+mU82lwA2Mha9w/wMB1Pue5znf/80kxM9kQYsXedGf4yMYjlTZ07qsQ+41N5Kk0mGi/tJJysN7h4q2nVNGH9sOX8gF1QeQaFAdNroNJznp0ntHPl2AzWuyaRFeQBy0iZMI6Qzk/X7ykGuRiaCIJd3hSYoFV3Hsu5jOsnZsp4KVTxpMd6AyKBxNxBpyWbdnmJwjyQpKoSgiEEMGxJFeOIwxiUE0NbUggkVE2deg/pEJkVVTRw6LhEd2MTurRnoiitwxo9mbLCGgq3fcJwohiT4A5A4+kYShAI27i6g6uBmdpbJGTIyDRHwSJzGlFgT279Np6ryIIu/yiRi8s2EqQF5IEG+P8i77ieOnl0LlmEe8yg/vyakx7cCAkhOnKe2K5K6AhyFq8/Z6ILKo4keyhBfK0XZx6jv5XuHoQOr0Yxep8PgFBC6n4nK1RMvrYLOTjOS82TWt+7HcypIrfvYbkPf3EyHUzglkELrgberAkOHGZCwO5w4HfZT5wmiDAEBJ+CdMpkEjyp2LvmKCt/R/OKuabSlr2DRjnaiE0Nw04C+qRG9Q0Dslk/m4oa3uwpDpxlDQz06u3RKdmRqAnw9sJpMGKtOUNZmR6U4aTZydmUHvwor+9Jjo2zbKg7Kx/DsL67DU/wuCfQpvLwJ1Npp1500FRnRt1rwDwrtOcS7wrnwwF07hPsfvY6O/UtZ/m05ZzwKSwXL3v2AXc0i0alJOCuOUd7SFZxtam2kVfIjLSkQQSaBw47N1p1iTxARHHZs9u5juZaI1GTEqjxKm7v2+rK0N6Nz+DA4ORiQUMhEBJn8VMSnTBQQZV0vsOAZx6RULzatOoQ6Koq0W+4g2bqbNUcaiAmLBhSEDEpFVV9AcUNXtJ6tQ0ezxZ1BSaEEpg0hzF5PXnFp18VtBmqarUTGxxOcEEGYpo19W7fR6gQw0mmy47Q7BxyYzsBBVcYa1uQJXH/zZLztjRxJ30zm8TbAQVNFMScajOCXyJhUX8pys7vC+JvKKah3YeS4NK62LSMuGAwHAoGJQwlxlrNpzSbymwzYzGZ0lbms+fR9NncO4eE7xxIdHoKpeDdbjrXgpjaRuXsPlrhp/GzmKNxVDhqObmblphxMojshUaFYj29lxaYcTIIW/+h4EmMjsJXtYfPRZlzVVo7s2UlHxFQenDUOoXQnCxcuIb3KScLwCfg2HuCL+YvIadEyaMwYIj3dEA3FHK2WMePOO4jw88BUeogKIY3b7hiGqyDgExoOVQfYnFWHRuMkd992mgPG87PbJxMcFomvpYgtu45hVmtoOraNw+0h3P3gncQFhxIkq2Xd4oXszq+jtVlHWeZWsioFwgelEhngdlnCh6+0YLimQ4v53e/fIeNEE0Xpm1m5ZCkbD9aRdO0dJPiW898nn2BxuS/XTR5GfLCSI9u2Ui26ULVvG8Xu43js3gl4K6+cvrwvwXCCdJYPwvPPPMubf3+rp2+b3URNSS75xdV0WgXkShFkWqIGjyIl1A0BMLVUkpdfQptFhrtvEDGx0fhouwx6nTU5bN+dizJsMKNGJaNqzmPbrmMoQ1MZPjIFP7WIubWKvPwSWk0i7r4BRMXG4ucqp7O+hKKyekyoCIpJwl9qoLC0BqvMnbD4BMK9NZiaKiiuNxGZkoi76KC5qpDaTm9SkoJOvdyW9lry84rQGQXcvP2JjI0jwL2rvXNa2ijJy6VSZ8PFzYOg6ESi/LsHEo4Oig7t5XBpJ8FJQ/AylaMTvAmLjCUy2POyeBkUFhSwauVKXnr55ctw95501uRxpKgROw4cDglJEtD6RpA6OA43mZ5jW3dQ7zWMySPCUOCgqTiLoyVNOFU+JKSlEdlbVrTLyNGjR9mzaxfPPv/8Ocv0XXlOw+mwIyEiO8cuGZJTQhC/fyvyQ8//IdeXpO7NRK5wrjTl+T5ISCAJXImPuy/K06PR7MuLI8rO39b+0Bf/UirOha5/NSjOSUTh6l5rEhCu2G2O1SrVBd+FHlpgNBqZ8957qM8XXj3AZUUURRobGykqKOSDOXOw2a4+15YrGUEQqKutxcf3/NlqeyiPTCYjPDziqkur+L+ETCZDJpNTW1tHVFQ0loG0iv3KyR7Hbj//Now9lEepVHLrbbMGguGucAoLCujQ65l+84zLLcpPktxjx9ixfft5y/TboNluNWOyWL/X2ofktGIymi/xdqsSNosJk9X+k1mfGQiVv3TYHRd+Gy9oZXV21FNc1YoglyHZbdgFBZ6+QQT5uXVrno3inUtYsKaQ6Ft+zn1TEi7KuU9XtIMFCzZgiZ3BLx+aTO/76v9AnAaObviSr7bUM+qRx5mVFnKlzlMHuIq4oPKIDiPlGSuYvyyL0GtuYVKcimO7d2KMv4NnH72RQJUCdw936o7tpX3ILO67SAFcPP2xV2awxzycx77nj7ggohpPrZySrHTcZjzAbf1yUens3eUHOIm9lrUffonshl8zPb4XvwFHGUv//gn764yIooQkhDDzhWe5NvLqmipceNjmGc3osYMQLXr8Uydwy+33cO+tSWR+8S4r0rty1QfEDiUp0ud7rbRrApIYkhSKWn4pza4ywhOHEhPq0U/jVCeVe1Yyd/E2Wvrlej8l7OSu+Zh/fb6ZqvbeS0i642SVS8QnJZOYkETikEFEeV9NwQhd9GlxXKlyQaNR4+KiBmT4RkThpTBjPJWQ1Y7TeVojLDloqymmrMGKX0wCYZ6neyE70J04Tnl9B2rfMOKjvXE4u71qJQv1FZXo9AbQ+BEZFUK3gwLWjiaqa3U4BAFUPkRF+OAwmhEUSmToqSytxyyJuPqHEeqjobO2mJJaI95RCUT4aJAkO06n1OULB9hNbTTUtyB4+qM1NVBWq8czLIaIAHcsumpqdFY0Xr4E+ilpPlGD3i7D3cefAC8XTLV5rPpyLluVN5IwIp6UiGC81AO7GQA05exkf7UZL7UrcrH3OZmtrgmP8ffw9ENDf2Tp+pe+pVUEBKeFhhPF5OfUkLsnn0F3/pI7xkZ9VwDoWvbSk7F+Fbk6kdb8XeRIY/nzq48Q7SKAo42j23dQ1NiJ7kQ2hxt9eezXv0CUiYCIXNCz/ct32WaOYcaMGwkO/055sLdycPm/WJzp5LZfvUxchIydXy2jNeF6bhuj4tjG+WwodmP2s/fRmJnO0XoJQ/FeDnUO4uU3niHh5MJo9z9thdv411tf0BozhWtilRSm76ZEGMSv//wbUswlLPrbx7QPf5Q/PzOJlqI9zPliI+F3vMwf7hhMR/0JattNWGRVFOUUERgYMKA8gK0xj22HGhk8cjCH1hac05zR0dCIruEYyxflYFEEMGTCBFKCXa+6eehFpFW00VJTRvahfezae4QGEzidZy3OCSL2tkJ2bC0hfNoDvPDAVIwHNnZnzZYo2vgFyw51Mnz6vTz525d56ak7ifdW4XRIiDIB3YkS9EHj+OXTT3Dz+GS8TuuwlF7x3DB1BOg60IaHQFM521d+yOfrj2KX+RIWG0ry2JuYFN7Brk25BEy6j+ceugkhZxs7itq/6xa7a9Q3JAo/hRWj5MuYmQ/xmxcfwqcynU2HK3GLGUaM1kCdzoiEkqQJkwiQ6mnoTrXtP3gio6ID8E2cwO2zpxHrMRDfg72DjF27cMaMZWSMN4LDiXAODwibVwKDQ9VItjYyV8/hhWdeZXvF1ZcNu2/KI0k45S7EDJ/M3Y++yN/e+jW+R/7LH/6xkkb7aVeRHMg8R/H8678m1VHI9ox8OkxmzGYBrGV8uzoTWexQIr3kCEovYhJi8XZVIsoE2vPX8dY7K1GnTiYtpPeJo/fw8YwLbubAzhxKaxpwD4rBnLeD9OI6GhpsxI0ZikKbyi9f+wOjVaXsPJBDm8GM2XjmBiUSgKcv/l5e+IZEE+6nxSc0mrgALR16E04UqLUuyOXdubdlGjQuSk5tXyyI36XCGwCA6oNfsyFHRnK8N821TRjsNtqb6jGaLZwdcxsw7EYeuOdO7nroed564zniWrYy/+sjPcpd6fQtM5zQ9aLIlUpERNwjUpgwLJDKnFwa9HSlYeu+nOSoY/O8fzFnUQYe8alE+7shCgIYOtG11tPQ2jNplCSByiOIYKGEL+bMI6vpHLvxqBK5Znw4ORtWcbCgkXGPPMcEWSFfrdtHnSWMtDgRzLXsXPge/563G1VkCnHB5zASSF0RjJLj5L0EJMRuhZBOBXEJ3X/LzlAUCefAEstp2KmrrMViKmP5nL/z7rxNVLbVs3PJp6xOL+2RHFmQyU85FaujEhgUEYD6EvszXgr6lpNUJuC0OnGcjArUV3O0sIWYYUMI8gScckRAVCqwFnzDf77MJP6WBxkV5oLZqMdktYNHEClJbuR8/QXbC1sAEyeyj1LeYkIQBDTho3nqr68yybaVP782l+MdvUkiY8ik8SiL97C/yY+hYycybVwAWWuXY44ZRzBgP76Z/3y2k9DpjzI2xgOLUY/JBgIiIgKivFshBAG5KMApJ1cJUQBRBiJyNHIbzTW1tDvAoSujsskKQvfvFwTk2DEZTAx4lQHIGXnvH3nnnb/zxt/e5G+v/IxE/whu+/VfuG9KMmrJwPGDOzmQ34CEiaqCAmo7u56cqaSABu9x3DU99apL2XHBYDhL5SGWLFjIxq3Z1HdaMOlrOLD7IKbw63jsoVuJdHNweO1cFny9jRNtSqKHpWLP28o3WzJoRobhxGEyitqJG3ENk4aEUJe+gk8XrmLnnsPoFL646vNYs3Q1R8oMhIy8ibtuiCXz83+y9GAzQQkJRPhqz5hIKrxcqD24H/8ZTzEpQoufRycH9li44enZRGpAVItUHtjI6o17aXSKmKtzyThWTktNNnt2ZVBndiN+6GBMB5cxd+kminQQO2QE9iPLmLt8MxUdrqSMHUWUtpHNixbybXo+tZ0ihpLdHK2SEZaWRpSPO9a6DJYvXkdhrR2/uERC3H/cOMgrLRjuJK0nslgxdy6r9+bSbFERFRdDiFcdHz37HF/XhTHj2iD2ffxX/vrhN+SXlFDaIDL6jru5JsH7ilKefgmGc1oMtHUYsNqdIIgo5DIQRFzcPNEoBMCJsb2FDqMdZHJcvTyR2io5fqId35gEPM01VBtdiYwIwEUhYu3UUX78OHp5IPHxYbhIRtraDTiQo3HzwF2rxNRcS5NBwNPfDw/N2VYsB41l5YihsfgqAamN8lIDIbEhpzwbTLoTFJbq8IpJxMdWT5VeiZ+3CqfdCTIl7h4eCJZ29EYLEgq0Hp7IbXraDRYQVbh5eeMimqguzKPW5k54eBBSWy02Fz+8Pd1xVctxmnQU5Zfi8AwjOiKwO23kj8eVGs9jtxrQt3dgdQCiAjcPT7QqJw3HC2hziSI+1BVLWz3HC0qxeYQTHe6Pu6v6ikvm+73iec5GVGnxVp1v5VfExcMXl9P9avyiGXYqC3Icyad9pXT1IWHY2NM+ccdPc+aGcC6+wUSc0xtchn907HeHgidRsZ5nlND4RDLU5+QmYjEkB/ZyGaU3arfTjtVnHaMhNGUEoScPvRPOOF3U+JA03OdcQv7PIldq8fY7+32RERA/mIDuI7VnEIPHBv3YovU7PXrKqykY7H+dgf17Lh0KheL7BcO99+67A8FwVzCiKNLU2EhRYRFz3n9/IBiunzkZDOfn53fecr0Gw8XHxQ8Ew13ByGQyXDQuNDY0kpSYNBAM188IgoBKocRkNp+3XK/BcDfNmD4QDHeFU1hQgE7XzHXXT7vcovwkyT56lN27dp23zKWzDko29E2NtJouXb5MydpJfYMOq6O/VywlLHodTS0dXCh5ygA/TfryRl3A2uagoTiHkgZD1/q7WzCDkqJxVQo4zCZMDtBoNciwo6sopKiyFacgonb3ouXgF3y2sZM7X/szdw3y73lpp4m6ygYE70AC3S9+fmWoPcT8f/6bLfZJ/PdvjxPsctbkTrLQUFWH0z2AIM+LGYJKFG/9mHc+3knQzOf47YPjBrK/XRIk7BYTDkGNSnklrfD0nQtILSJYW9jz+Ss8+/L7ZNXaTiV1qti/lP98tpYGC4AMBa3s/eKf/PvLHbTJ/Rg6bAgyfQ0Nnb1PZp2NeXzyyou8v74YOyDZrJh78YM6F9rgFAbHedBUV42l1wxKx5n/lxf556o8Lm5GIBA+ZDIx6mbKGzoHAp37jIMT6Z/z1KxbuXP2bO6YdRfPv/4VFb1Vv62ODR+9zuv/mMPbf3mFTzZcbB1dGVygURXwT7mWB3+ezc6X9uDp509XI9FBadZmlqz1YvydMwkO0eAeEUlw9EjuuOYBrkv2w1bmj5ebmnNtLSb6J/HIn95C8ItAzv+3d96BUZTpH//MbE02m94baYQWWujSO6KIWBC9U8+z3Hnq6RWv6f1Oz+4VGypyFhQRRJrSpfeWhATSCOm9ly3ZPvP7IwECCRCVkmg+/83uOzPv7rzPvO35Po+VpJUfsE8cwkN3T0Tf8SkX4I5/gD86rdjxG8A3jnv/+ipO7zC+q8+zxiuQIF9PshU9S8Gdx0pVZSOhI29j3ohgHHbw7dWfkHaOFzIZK9/gg5QIFi5+At+05fz6hbfwjfkPd/Tt3JPvKnRqRBLQbyKD/b7haFoOdw4fjVhfQ02DjF4qYFdKKePDekNJMQ36ECbGhAIgIyELChSWSlL2nqCwQU3CmNHEB+oACXNdLbU1NSi1/iiLD/PFV2vJC7cTE6Jn5OjBhGgVYK8nKzWVnNJmwoeMITHG77ydDVmWQbJSmLqXk9X16KKHMnJQNDqljKW+hurqGhB9CfPX4WgoJTurAEJj8aw/Tb7Zj+GjE/BW2SlJO0xSVhnKoL6MGT0Yf5WMJAiopGYKsw+Td7KSwITRDO8X3O2CkV8z7FbsDjUJs+5keuIl8h3YT7N10zGCx84nAmDAUAarPmLrtixu7zuyW+1cdWqwqfKNZvQgP3KPpVJjg7qKLJyxt3DfODcObT2IASgrq0cXEEpIcKs9CiKio5qk7XvJKiziyJq3eO5fyyk0AcjUZ23nzX88z+f7i3EJKjRqNSqVApVSiUKhAFsV21atJbVahZecz0evvsymbMP5FRNEpIZSMvLKKMncwzt/e4IXlx3CjoAhdw8Ln3+OJbvykABj7j4+ePkV3n73fRZ/8jEffbaZ4voGDq36gr05TYj2cravW8ex/AZQKlFipeD4QY4ezyU/5WtefuYltp3qXhlUrylOB43l+Rza8jGvPP88b3+6iYKmDgbhlUVkVbrwC2n1N1D6EhKkIj8nm+6m6OncTE3hQ//RQ7HnJ5FdVk9FZjaaUbdx47hBWE7s5FhFHWX1TfgExhNwVootIys86TN+Ngvu+zVPPDwbc+YOUooaAQURCcPoE+iG3SYT2ncocYFe+MUmMmncIAJVMgV7V7HxSDmB0XHE9U3AozqVbQcyOW/lXZYQPCOYNGc+j/79BZ68JZJd777FxiI7QQNGMCDUA7vFgQsI6JNI/2A7xY0B3PfMW3z45oM49vyPtadVjJ89h7n3PsmL//wdE3v7gMOJS1YS2Hc0N9/9c57401P05zg7juRc2X//R4SsdCdy8CSmjhnI4N6eHFvyHL/7v08ouGCrRGo2Y7KLaNzOeLOpcXNXYTUbf6TGg0BUv1HEUsKu5GOkFHoxqL+WiOETGOCWz4bVx2loaMavd3Sbc2RkQY3O2wMF4O0bho8GjLbWpWuNO+5adUvCXmRkqSXhlQwgGck+fISM4irSmWnb0AAAIABJREFUD29jb1otYx78Gw/NiD8/rJUMgkqDm1oBeDJ28nSi1BWcyGkCrTs6N/U5h0ONFq3Gnz6DE4kO9kanNJC8+wSuwN4E6QBBid7LG3f1mRqJaHQe6AClezBh/h5Yzc3ttCk9tCCoPRk8eQ4zJk9k9j2/46W/zKbx0NcczDSdV05Ua9GKTuzWM6s8DqxWJ2o3Hd3Np6XTq7CaqD6M6KvhqxWforrpzzwgAsHDmDbMjxfWLidswS3cF3HhiFXmTOrOllWrtt5Y8gUlORucA1nC3mxCFTGF2++9j/CLBlaRz7umLLmQtQGEBmpBbuZ8f3EZZBnhzIcOF9bmaopKq7FLoOnoNdLmfFkQerLBfQc8o6KJ9CzEy/OC5ZrgEGL8BUrKqoEIkJuorXEQndib7ubT0vkFdkUkw0bGYzhdR9TouNZG5MWEaaPR1mRhCxlC290cWZJxOZwt+SZbPsDlcp6LCirLSC4HDhcIggKVYKOhrqllWKbQ0++GodgPfcZHq49hsBo5lbSfpOzKdkvZ9sZ66hwy4CD1aBruQ6Yyva++Je+ly4Hd1WoDMkiSE4fUGmfTI4Sho+Mo3/gBn2zNxGxtIn3PTo6erkEWFUgOJy7XmexvMpLTgUvuidF5MWz1OezfnUyNHcBE+t7TxN39CJPiVCA3cnjNElbvyUVyT2DapH4UHT9EBeA8nUGaOZypUwZ0KT1PZ+hEZrhz+IoNpJqjuGfuaHxas3hp/d1pONVA4l13EuvZ8plsr2f7lx+y9cgpGu3e9B0SxPFVn7D9SB5G/Bk4PJby7V/wxbZjlNU3E9x3BLHqAr7+YhVJeVbCBg9nYL9++Fgy+WrJxyxfvZ1qbW8mjBuKr/bcX2w3VXBy5xb2ZZZTkZNCniuaex++m3gvgeyty1i29TAldWYCYgaiyFzP0k0HKa5pQuEfz+DoICJi+6CtOcqyJUtYs/Ew5oBBTB7Xj4o9S1m2/gBlDQLhQ/vTnLSalRuOUGlUEjFkCNE+13+A0dXEcI6aFBa/8CIffrOPzKwitAk3cc+8EXiJgKuQz597iV3GKKZOHkB831jsJzazNbmA1KPp+E34GfdN7U0XSgzXKTEc8gX89rHHZZPJdOHHLTiMcm29SXZJbT6TXHJTba1suaCoJEmtX0uy1PZYOncstZ4vybIsO5rl6vIyucFsl9te3lxXJpdUNcqujmskuyyNcklerlzeYDnvvHPXl2RJan/cpqRsqimTy2tNZ89vf67r3PFF6nGtycrMlF9+8cXrXY3zsBvr5JLictlgcbb7ztpQI9eZzn0uuSxyVVGeXFxtkNuXvv4cP35cfvvNNy9Z5rt5nig98PO54DNBxNOvvSjsjBbibCKpM8fC+ccIYssQUOlGQEj7Ua+7b+glsySLWi/CY9pHuG57nzNBPM4/PlsSnX8oukueK17k3B7aovLwJdyj4+803v7nbVYLopbAyJhrUq+rRXcbZvbQwzVB7IQotF3PY7Va+XDx/3rEcF0YURSpqqwkIyODTz76GLu9ZwH9SiIIAmVlZej1l3YXamc8oiji6+fbI4brwigUCqxWC1qtBv8A/x4x3BVGEATMJuNlY/N1KIa77fbbe8RwXZzsrCzMJjNzbrnlelflR8k1zQz348ZJXUkeeSU1XSrIYc+u09WjM5nhvrPx2MuT2LIn59rGFZbtlGYc5Vhm2XVovC4y17/JIz97iLfXp3dL3cn1wGZoxGS/uHHLNhN1FWVUVjfhuOJK4GvDdzQeidS1i3ht4UpOXcs5qsPI4RULWbz2GA3XXBetoP+M+5g5wJ1G8/fLufpTw1G+j1cee4QvT1xECNmUycevP8/CZWv59K1/8upne2m8uglprwrfzXgMaRytAGXxAfYmN1ylKnWA2ofZT7/Bq4/PJOB6aKJFBRqNumeM2xls5Wxft4pdGQ1tEgC0xc6Rz9/im+p+PPHHx/njLyZTvG4xq1PqrnlVfyjfqSkWHkrHfdxdTC14hX27DnHPmNnnVJ+SlbLsFI4kFRM6bixy6haOlqkZPec2En1q2PHNFrKNfkyZN4dBIS3bnrKxlIN795OW10j02JuYPtiHouNHOJ5vImpwDCX7D6EbNZcJYRaO7U/C4BnPhPGD8FKApSabnZu2kV4pET/+Zm6+IRYV0FiYzLdb9lDjkcCcuTOIVNeSdugwuQ0a4vsFcmrXdkpVsdx0+xx6+3Qc5NVcksKWHUlUu3wZd9NsBgaeMxsBwFDCgT1HqHWLoG+wxJEdB5GjJzBnxiBMGTvZvCcb/YCpzJk+CP1PyuIsnNh1gDpdIBFehVzgmdtCczY7dmURMesJfAF692OQZyW7dqXzwIiJ3eoF1fm6Oos4ViYwtN8w5t6YQNXR3WRWtfledlB94lvee+Mt/vfZBkplD0zpa3nmD0/z7vL9NGu1lO76gOcXbsQgA015LP90DVXeiUwb6saa1//O8v35FCd/zdv/WczKNV+xeechTubXY2soYutn7/HZ5nSsAtSfWM//PjuAfsANDAwwcPhAJhZsZHz9X175/AQRQ/tTun4h76w6hs1l5uTmJbz++kJW785C4e1O5pr/8sqHO+lI2mbK2sQ7y0/Se8qNxJj38uI/F5HT4ERs8xZ1GcvYt/oD/v3vRWxMKcfdw8qmt57mD/9YyL68ZnRCMZ+++jyrjna/t+kPoS5zP8fK1YweORB3Uep4iFtZTl6tgHfAGVcVL/wDNZQW5NF8Det6Jeh0z2PMPMnp8go8ysrw1AUhlO7iYFoBo2a0angUeobeMIoYvxMMmXUXd472pca/ln3PHiP6lruYG6qhj5TD46tSqbHOpWT7l+w6aeHmIRaMsg/+SiOnKuGWCcPx+iST4FG/5vW/tUi6kcOZlBhFYT24DDkse2c13r9+hwnD9DB8GDcCAgYsil5MmzuGMb0FCiO0rE3PpvGBEUwbn8CKzGZm3bmA0X7Qqz6Fpw+cpJzp9G77I6UyVi9eRlnYPGx19aj8QqEij5x683mJrBRhQ5k0LI7k9ARuXXA7McpGzCkH2KSJYfb8efhYh1F47H7Ssgph9E8jnrXLUMDewwXET3iAOJ/tyLKIQtXeuViyW7G6BFSaM/+nErVGibPBgg24iHdPl6STPY+ZjNN5NFuclJ9OJrdGT+8QB0f2J1PbdqIniIii2JpjFNx0OrRK5Vm3MnedHrUoYzc3kXc8nVIzmOsrqLPquPmp53j0xn5oHC40ukh69w5te+HW6yqxZh5kf76W8HB9m28BPBk+cwohTcdZtXYLuU1OlEKLwE4QRURBPJvZzUvvieBy4bpwybA8h6PZDTidRirLypFCx/L0C08zKUx3NtnVmTsKoqKlTgIgiuj1+lZhHyC6o9drcDraSDB+1LhI++YDVu3O49SxtXy+bCclTZUcWreMAydLzxMQiu46PFQOLKYzKz82LGYHbp7e3U7P06mex1lbTGZhM1N++SemxCoAB4M8i/n9J7vJrLiZCeFtXHkE4ZzPJ0KHzpQtjdmGyz2UsdNm0auN56dNlgGpdbx8fhJeAFGQsZrzOXWqlhlBbVIpSHVsfe8V1pbH8quHb8KvJoXThTKy0OKnJAhtrtNap3bTWVFEIZsRQ0cx5+Y2uR0c9a2ntTmjVRzXminrrFDu7C1ouedPw5FUIGjIHH4Z3IxLEpBkLzQKNZ6+AXjrNee/oUMi6BOsIr2oBIgEex0VVU7ip/S/pANwV+SyPY/sMJGxbyPHi/WERZyZYKuIiB+Gf/1BvtxyHEPrer7dYMBgMtBkaFGjm4wGzMYmDKaWY2NTE2ZDIw2SGwOnTUJ7/FNefXcN2QU57N26gX3pFZiazRhNBhobTecmnNZmjIYmGhvrccWNZ0asieX/epHVh0+Rn3GAVSu2U2UyUZRxnHyjGl8fJdUVZVTXVlBe1oyh0YDBZMRklgAnjY2NmM0GTBcOskMHMX1sKIff/z8WbT5OQc4x1q3dTm5lLYYmIyaDoWVc7mjG2NhIk9FIsxWwmmlqMmAyGWkGJKuRpsYmTEZTt9Plfz9EwhLGMnXadGbMmMak4bFoBQWRg8cyICoApVTF+jf/wZsrk7Gr+nLjTSOpOr6bDJNE3fEkTtKfG6fGX+8f8Z25rBiu6NAqPlu1m2q7Es/gGOIjfFA4DKTt30lOXTN1ZWXY9FH0DbSxe+NG0mvNKDUBRIapSN6+lWKjDVEVQKificPbDlBjciK7RzJu5jT6e5s5uPEr1mxOQhEzjil9VezbuoMCowWrQ0FYdAwBehXVqd+y/uApTA4b2rAx3DV3FM2ndrF29UZSSkRumHcrA0IC8PcRyNy2hh1ZBiIS4rHlpVNpbKQgv4gGhwM33yjC5CK27j6G0Snj4RdNn9iANuGk3IgbOAC3+hOsW/kVu9IaGTB1Kl4l+9mTVorDKeAZ0QePisOs35+O0akkMLY/quK9bE/KwyGpCIjuRXP6dg6k1+JCQ0ifvkR6X3kn264mhjtDQ/4RVq/cRIEFzEYjPhGxRPiZ2PXZl5xS9GH8DXFE9huAb00S2w+cJON0LQNvuZ9bh4d0qQRXV14MdzWwmWST9WJSt0vgsssWi1W2X3Cq3WyWbS5JlmWX7HA5zhfudRbJJTssJtni+B7nXiO6ohjuUkgOq3zeY5Zcsrm+Rm402a5bnS7FlRfDXQ3UOr6XC6qooiPVhMr9zMhZQCl+z10DQUSp1fXEqL6CCErN+ZFbBRF3n4um/+sWdNg+5Na5htzRJlcP1x1BEFqezZnYKj3P6YoiCELHG7wX0F4MZ7Px+dKlPWK4LoyoUFBRXk56RjpfLFvWI4a7wgiCQGlJCRrNpW2gnfEIgFqpQt3BBlcPXQOFQoFKqUIpKlqeU0/Hc0URBAGlUnXZfYZ2xqPVarnrnrt7xHBdnOysLBx2O3fMv/N6V+VHSWZGBjt37LhkmXYz6nbjZ8mF0+lCliVcTicOp+vaankuQHKYKDx5lEPJuR36pv2UkOTr+SR+3NgdjsvOJS+7oCTV57Bl637yKky4+Qfi7+mGgJaoxFEMjPJDiUTJ0Y3sqwxg1s2j8b3KbrHVJzbx4p9eoybxj3w0LO77rdT1cFWQbAYKM0+SW+siLK4f8dEBF03J0lyVR25pAy6lBxFxMfjrut804bJNXfQKI9LXyOblK8lzBTNkUAzWU+v42xPPsCGtFhCpzT7KwaQcmq6BzDJ42J3cM70vgtQjQu5SOBpJ2fwFK9ZtZN0nr/D4Y39j3YnGDovaSvby5r/fY1dmIcmbPuHld7+h1Nr9nubl+wmVJ7EJAwkL9SEqLp6YuCHc+fBjDLQe5avNSRiAoT97ltf/cjfR18Szz4VMT/DBrobDYUfwH8Qv/vwy7y16gRGk8u2B0x2UNLL7s0UcYyQP33sHD907Hce+Zaw8WHnN6/xD6dQ+oOx0IcucDcWjULijcxORJHA2lLFlwzpO28KZ87O5RLmK+HbtBrKa/Ria4Efqpo2Uagdw9yP3MTSoowSHdgqObGXb4TwMVgeBg2dwx4zBuIsOqvJS2blhE8drPJj9i0eYFNcmjpaoRGmrYMuyLzhc1Exwv3HMmTOZsJ5x3HVB5R7A0HGBiEBzYT2qiInMndyvfcHGbPYeLqbXHUNaHEHDezMgwMCOfSdwTgnpVhvTnc7PI0h2jE0NNFsaSNm1khRrLDOmDMFX2Uxp0la+3p6BWQIkG2WpW/l86VqOFkskTh2H7einvPHx7g4m+C4yV73Csx9lM+b+p3j87mGcXPxXnv/sEKd2f8xr7+8h5pYHGOE6xBtvr6KsbcVFAVEj0lzbgO/QG/nZnT2Gc30REB1G0nd8yrN//A/5njGEenTQvGqrKTEq0fueUe544OPnRlV5cbcTw3XKeARBQJSsFB4/yNdfrmBLio1b//gP5o8KBn0cE8f0Ry+0bjd4xjNhZH/CI4Ywa+5Mxk25nXsmx1ObX0g7XWVTKl8s3YbvDXMY6A3ayCnMnx7G/s+XkKpI5N5f3sWQIC2e3p7Yyoupac2TJIgC9oZcvl76NebEu/nVrcPRdyWvwp8oLrsV9NHMefgBwk5/xp+f/5ALM1HKLicOl4x4NlmyiEIptKRwueY1/mF0btgmS0hKPX2GDGfiyBCm3R5EgP7cqa4LVGVOSQZZOpvYSqPVgiS1X+KuLCG31kyE7txwLKpXJJjTwCcWVekmlhyQ0EhqNAJnNwMFUcRWmcXWdQ0ETI7jtqkD0PRMgq47Cl0ACSMDAOjtSuf+146QWwF94s6VETz0+GgcNBvOrC5ZMRvtePn6//j0PACCQgBBxMM7iNDQsPMMB0AhigiieFYEpxRFBEE8m0ZeIdBxhgFvX4LcBUoK8s+unFksVrQ6b4o3vchrq8oZNWcBUxJa3dVFAAVI4Nl3Gk/8ZhZFy1/ktdXp3e6t9WNDliVcbeKvuRwqfMMHEBHcciw5nTglIDSGhEg3SnJbEi3TXEVhOfQbPJCOZsRdmcsbj62R/OwsigvLyc7Oosx4fuwyyVRNXn4hZRWFFJWacZmqyc0voryymJJyC5KpmlP5xdRWFFFafYEPVtBo7v35FAwHV7AmuZja8nS2JVcwasECEnUGCgtOk5WTSUZhFbWVmRxPK8VYU0BeQQkVxZXoRvycZx8Zzu7Xfs8rXx6m2mjtWb6+Tpjyd/DOy2+y4eBJcjIPsSdbyd1/eoRBHoCrmCV/eYi/vreLZiGKOXfOwpn5LbtyK8ncsYd83xu4bVr3SzdyWTGcsz6fo6mFaPwi8PNQoPYMo1eQ/qzVWSqzSSk04RPsh7dfKAHUkFlixCckgIDgSPzkCjIrLAQGBxIQHElkiGcb0ZOC0IQRxLk3kJldRF1lDer4Wfx8/nhiIsMRqrJIKzDQa+R4ohWNWNyD8RNqKGkQCPL3Qu8Xw+iZU4hV1ZFbZMC7VywRfrqfxDJ2lxPD2Zs4lXyAQ6m5GJ06hsxewNS+vq1fmshPzcIWlMDwQeEExCUQq67ieFoOZUYtE29bwIQ47y713DojhhPkC3wQnnz8CV5+7dVr7tvmdNhxygIatercnyhJLVFrOpEr5adGdlYWa9es4a/PPHO9q3IOWcIlyy3BUS5fGKfNgkvQolF3vWhtqamp7NuzhyeefPKiZbrMsrpSpe4o38n1qEoP3xdBRNHp95yAUuPedRrgBXTmZ/S0zm5Mj5/F1UOhuPzeRzvDt1itvLfw3R4xXBdGFEWqqqrIzsxk0fuLcPSI4a4ogiBQXl6Or8+FCXjPp53xKASB0NDQnsxwXRiFQgGyTGlJCRHh4T2Z4a4wgiDgdDhwSZeWfLQzHo1Wy623zesRw3VxsrOyMJlM3DTn5utdlR8lmZmZ7Ny+/ZJlLi+GuywSdpvtCm5SOrHZHVdkv8blcOBwXr5msuzCbrP/oN8gS07sV6jenaVHDHf1sNvtl7WFTi4YyDQ3lJB6+CBHUjKpqG9x4TNXZrL2g9f596LNVPzgViPTUHiUz998iTdWJv0wY5RsnNqznH+9tJCdOXWXbNBNRUl88darvPP5XjrMOCTbMRqaL1mf6qydvP/qayzbnon1h9S7h25Fp1YKa05u4avtxUQkxGHN/ZaVa3rz1Is/I1itoTF7D+sKXNz+5K0/sCoCSo1I8ZGNbA2O5w8/H/P9LyUqESxVHNi2FeWEW5nZ/+JFFSo1VWnfskH0564Hp7X7viHpK5794ARz//4SM3p1/HcpRBc5+zdQrxzB/Nnfv9rdGXvjSZYvXE62SW4Jfi/LOJS+jL3lLuaM7HX+W9pVzIZFyzhWaUEUZSQhmBkPPsDYiO7l3Xb5nseaz4pF/6MuYjJzpk9l7vz59FeWUWoElW8sNyT2xVN7ZVbr9SGJDB/YCw+1+AMXYRXEDRpL/16X37X2CB3EDYNjcLvIRp0+rB8TJo8jxufif5Vf7BhGJYSh7DAT2k8DU8kxtm07hUOrQ++px0MDdcWZ1Ls82jUyuTGbPUcr0Oo8cHfTofPxw1fX/dziL9vqZXs5OZnluN/Qshyq9uvHXY96Y2uVnDslCUEUcJkaKamsRfIIJDzI8+xmmWxpoLi0BvSBhAV7n7uh00pddRVNVgEPb08UDgdKvRqHBLLLRm1lMSaTC6/gcPw92ngdWBspKa3GpQsgLMQHlWTH2GTAKilw14o01ZvwCAlDJztwyS2bXU6HkeqqRuw2B1rfEIJ83NoYlYRTkhEFAXtzA0VldSi8QwgL0CFIThz6GKZMi8BN28YwZImGiiKqmhzo/IIJ83HhkuSWYIQ4qK2sxtxsRXD3JTjQB7UIDks9FeX12AUN/mGheGsUILuwmk0YTVY03t44G6owWmUUahWiKOLu6YPGYaDeZEWSFXgFhuLZRb0nRV08D//nZiYODwSgKX87n62pZvqo9vmJHOXVeE24l78+OOJaV/OKclnjEXT9GDfSn9ff/huvKf/EA/NuIDAo9GwSIkEQcNQXcGDjWuqSD3O8RMVtf/ondw31pjb3ELuPFtBQkcWhTDs3P/40tw0NBFcjh9d/wf4SNeHeVk4cy8Tu248bb5uFpFBgqTzFt2urSDuWQrV7Ag/+/kkmxeiozz/CriO5NFbmcPCkkem/+SsL+jTxzbvvsKPEg+GJeg6sz2D6P9/n/pCW950gitgrk1n0wqdIfScya/ZNBPi4nRdUXBShuTKL3d+spuzwAdIbAnng788zK8LA0dWLWLy+jDtee4d5cWpwNXJi7z6yisrIz04jTx7M03+chyiKgIjSXsa6N14mVd2PmTNvxCfAB6k8ma9W78fhE4RQm0NecwQLHrmfBK8m0jZ+yPtfnWLQLWMo3boFg08cnuZ8yt2H8dSzjxFvSOajfy3DMngeD/38ti5rPN4x45h41rezmZTNe9CMfpLwDjpsc2U1jU1qtm6swKHyZ8CwoUT7db+tkcsP2xR+zHv6dX473YuvX3mSR554hW2ZtW0KyLgENaGDZ/Lon//ABP1Jln65BwdNJG3YzCkpnvsfe4Kxmly+2ZKEETCd3sriD3cTMPoOFtw3n2DDSfLsISQOjkYrO1HoQ5g0/1f86S8PE1n2DS+9upxKyUjals1kWHpxz2+eZIpnERs2HKTBrRfx/nbSU9Kx+I3k0acfZWyUO1Jrfh9RdFFRUknw2AX85pF7Gdc3oF00flmWkEQdsaNu4Ym/PEmCdQ9L1x7GpQmkd4QH9WW1WJwC4CTz6w/5MsnC6HkP8oe//I1H54/HXyMgyTKiSqS+vARXr/E8/OgjzBnXF71Qzlf/fokdhnjm/3wBDzx4O7oTn/Liwo00qnyJDdVTW5BOTrWeW371O3771KPcMkhPaX49Sk8PfMO9UXoncMttNxF76T27LoM1ZzPfVsZy05iOY1Fb9b2I87JQUZDOhg9f5re/+xeHyrvfXlWnJitq//7c9/wihk/8gtdfWsizf6xGXPQfpkYqkWXQ+ITTp28oXkBiQhRr08qpxYeJv/gDY5RQmrqL3JpmnH7NOADZVElNo4S7VgXoCAzwRK3WoEWJLMmovYII9/NE9JvCIz+bwo5/bedw0QPcdO/vSBSg8sQ+TlU341SZcCjVREWGEBCkZ/TEqYxt0WLhKgNRsJK+7k2ylH156rkFhF5kPirLIrqgXsRHB+JNAIl9gzlaVYEBCI0Mx89djaBQgTmNNV+l4P3wAnp5qYAIhg0DnA2IItQkfcXLRYHc/KsnGRzauk+Wd4gNhysY9PwNLb21fgCzJsaweuVGjtfOYXJUGAFewQwcP5tJo1pEgc475hCzbiEHkmvp5cpAM3o6w0K7aJfTjnq2rjhI6NTfEXaRaUzgsJv5RaKIRq3i1klreOrX/2TxmhsZ/fiIbuVwdNmex1mXx+lyK4JCx4DpD/Pe4meJrDvM9kN5QKsDnSRxRgclKJQt6QaRqT+1i3dffpN95Tr6D4hEI8tIgF+/2dw4yo19mzZzMmU72c1x3DZvHG44WwRS8jnVqbe3JyqNDjetTGPuXha98h92FqoZkBCFlhZxqdMlo1Rp0LYL/aXEXaehPmkVH644dMkgibJLal2OlhCUKsQzntwuGUmWWxy7G+oora2jyezs4AoCancPxLID/G/xOkpaX6Quk4Emmx2Hw3G2pJ+vLwqXE5cLkGRkNOjcz7U0ZdgEpg3WcmzrUtYUuDFmSC/U3aRVVe9dxYamaG4cFnrRMgqVBm2r97x3QiIjYgOQrd1Pi3VZ47HXHGHpx1s4M1BzC40gMjCA4EAv4JyKVNn6cBVCSzoJre00K958hwzfWdw/dyxeThMWSW6RZrtk/KPjCRAbKKx1565//Iu7hvgAEpLkwmm109I8bSSn5hF8w0zGeJWy4s23SHGbzP23T8LHZcLiaondpla2pjhs82sEQQkoiZ/9BC//eRaZHz3HO99k094LTEQptuQ8bWm+ChTICAqx5XJtrx0QTr8IG/tWfMmJahvIzRRnnqK6WUIAfBJu5plXf0/A8cX831ubqHGBInYQI8JVpB870hrgQqKwsBzfviPpEwQtQ0sQxDbhAUVfxs8eS9Pmr8hwhhIf0U2SAptPs2L1YWLGTCBK3+ZhyBaK05NJL6hHxkZlYSF1tpYnbC/KpdpjOPNmDup2XsqXFcMptTb2LPovG0/b0bhqObZtN+ao2dx/53AoTebLTz9hx4kGQgYOI0TKZc0nS9iX3UzEoMH4Owv49ptvyW00YjJUcPxIGoQPo4+ugCVvLCa1zoWlpoCkvbvJqhGI6ReFLWcfGzYfoU5QUZ2+n3RDGPc8tIBYPzXG4hQ2rf+WnLomzOZqUo+cwKJQcGrfRr5NKULlH8fA3mG4q4wcXPMxK74+QKXLn0l33UuieJL/vfs5OVZ/+g+KxbPV2uuyd/P5kqUczLUTPTwRr8Ykln+8jORSJdG9gyg6sI4VW5KweUQydOgoEqO0pK1fwtL1u0lJTqdGcoeaVL5Z+Q0ZlQIDZtz484wWAAADVElEQVTJ3KEqvn7rv+zIF4kbPoHxAzxI2bKBkw0KHMUH2ZWn4tZfPcQIvZE9q5eybPMRDCo/esdGEdS6IqDTKchIzaLX5PlMjvdu9+C6nBgOF+lr3uLjFB33/WoBER5tukpXHu899hhfloQze0oQ+959gdeX7KSgtJDTRc30v3k+MwcHdbvMcJ0QwzmpKz5FVk4JFlGHf3AEUTG98NEKOMz1VFRW0+xQoPcPxkfroLaihmaXAq+gEHzVRtIPp2EJjKdPgEh5cQ0ekf2J9bOy9ZO32ZavpX8ffxoLjrN1TwFTnv4vT00PoehEKsUGkYCwcMLCQ/Hz0CAALnMVaUfTMPnG0jdYTWVxFRr/YNxkC80OCY3Oj9BgPzQKJ3XlJdQZbKD2ICgiHL1spCi3ALMqgJjYENxb19JthhoqquqwSiq8g4LRi81UV9ZhR4O3ryeytYkmkw2FmzchIcHo1BJN5fmkp+dg9ejFoCHx6Cy1lNc04RI1+ASHEaBXUJ2XRaXVnfCYSPzclTSV55FXUous1hMYEU2Evzs4LdRUVlBvsiGq9QQEB+Ht3tIDWcszWPX1Pvrf9WsSfWlHlxPDSXZKM5KpVEUxuG/I+WF2ZQuFycnUevYjMd4bU3keqak5uPyiiY+NJMhPf3bk0lXojBjuOqRVlOSML1+QH37qAzn/TMrD5kr5s2celp9befIq3rc7YZNTNyyUFy5Lki+W2bG7pVXsbnyvtIrCVZc8C4hOA0WnCti9cySuSC11xZlYoyZz59QBV/ne3YPyvZ/y/ops5r7y2CWXQ3vEcFcPlVKJcBklc7tnYzQa2bVjBzqd7qqk6xMEEYc2nsSQrWz84L8kB/vi5uZF3OAR1JzYxU7nT9tTWFTI5GzbR40imuZTu9md7WwX706hUFBYWEhhYSEH9+/Hau1xR72SCILA6dOnaaivv3Q5+QIL+XzpUirKyzslQ/3elROVqBQyVosFhySidXNDKThxOLvbYuXVocXNBwTkDlNjCoKA2Wymvq6OyKgoJFdP1LorjdPpZMjQocyYOfOiZdoZD4DrGj2MM0PEq9HDdW8EBKFjw+nh2nG5DqRD4+mhhx4uT3fbl+qhhy5Dj/H00MP3pMd4eujhe9JjPD308D35f/ir48bGJZQdAAAAAElFTkSuQmCC)
One method of calculating the approximate age, in years, of a tree of a particular species is to multiply the diameter of the tree, in inches, by a constant called the growth factor for that species. The table above gives the growth factors for eight species of trees.
If a white birch tree and a pin oak tree each now have a diameter of 1 foot, which of the following will be closest to the difference, in inches, of their diameters 10 years from now? (1 foot = 12 inches)
![8 x minus 2 x left parenthesis c plus 1 right parenthesis equals x](data:image/png;base64,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)
In the equation above, c is a constant. If the equation has infinitely many solutions, what is the value of c ?
Note:
As the equation is true for all values of x, we could have put x equal to any other number instead of 1, and we would get the same result. If we put x=1 in the first step as well, we would get the same value for x
![8 x minus 2 x left parenthesis c plus 1 right parenthesis equals x](data:image/png;base64,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)
In the equation above, c is a constant. If the equation has infinitely many solutions, what is the value of c ?
Note:
As the equation is true for all values of x, we could have put x equal to any other number instead of 1, and we would get the same result. If we put x=1 in the first step as well, we would get the same value for x