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S left parenthesis t right parenthesis equals 10 left parenthesis 0.5 right parenthesis to the power of t over 29 end exponent
A sample of strontium-90 will radioactively decay to half the original quantity in approximately 29 years. The function  above models the amount of strontium- 90 , in grams, that remains t years after a 10-gram sample starts to decay. Which of the following is the best interpretation of the number 0.5 in the function?

  1. The approximate number of years it would take for 5 grams of strontium- 90 to remain in the sample
  2. The proportion of strontium-90 that remains after approximately 29 years
  3. The number of grams of strontium- 90 in the sample that will decay approximately every 29 years
  4. The number of grams of strontium- 90 by which the sample will be reduced each year over approximately 29 years

The correct answer is: The proportion of strontium-90 that remains after approximately 29 years


    HINT:- The portion is nothing but the ratio between final after 29 yr and initial right now.
    Explanation :
    Finally at time t is S(t).
    s left parenthesis t right parenthesis space equals space 10 left parenthesis 0.5 right parenthesis to the power of t over 29 end exponent space equals space greater than space fraction numerator text s(t) end text over denominator 10 end fraction space minus space left parenthesis 0.5 right parenthesis to the power of t over 29 end exponent space equals space greater than space text at t  end text equals space 29 yrs; 0.5 is the ratio between final amount s(t) and initial amount 10 grams.
    so,0.5 can be defined as the portion of strontium -90 that remains after approximately 29years

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