Maths-
General
Easy

Question

Does a linear , quadratic , or exponential function best model the data ? Explain.

hintHint:

1. When the difference between 2 consecutive output values (y values) for a given constant change in the input values (x values) is constant. i.e. y(n)- y(n-1) is constant for any value of n, the function is known as a linear function.
2. When the difference between 2 consecutive differences for output values (y values) for a given constant change in the input values (x values) is constant. i.e. dy(n)- dy(n-1) is constant for any value of n, the function is known as a quadratic function.
3. When the ratio between 2 consecutive output values (y values) for a given constant change in the input values (x values) is constant i.e. fraction numerator y left parenthesis n right parenthesis over denominator y left parenthesis n minus 1 right parenthesis end fraction is constant for any value of n, the function is known as an exponential function.

The correct answer is: The given function is an exponential function.


    Step-by-step solution:-
    From the given table, we observe the following readings-

    x1 = -2, y1 = 4;
    x2 = -1, y2 = 12;
    x3 = 0, y3 = 36;
    x4 = 1, y4 = 108;
    x5 = 2, y5 = 324.
    a). Difference between 2 consecutive x values-
                                                                                   dx1 = x2 - x1 = -1 - (-2) = -1 + 2 = 1
                                                                                    dx2 = x3 - x2 = 0 - (-1) = 0 + 1 = 1
                                                                                            dx3 = x4 - x3 = 1 - 0 = 1
                                                                                            dx4 = x5 - x4 = 2 - 1 = 1
    Difference between 2 consecutive y values-
                                                                                           dy1 = y2 - y1 = 12 - 4 = 8
                                                                                         dy2 = y3 - y2 = 36 - 12 = 24
                                                                                        dy3 = y4 - y3 = 108 - 36 = 72
                                                                                       dy4 = y5 - y4 = 324 - 108 = 216
    We observe that the difference for every consecutive x values is constant i.e. 1 but for y values the difference is not constant.
    Hence, the given function is not a linear function.
    b). Now, difference between 2 consecutive differences for y values-
                                                                                             dy2 - dy1 = 24 - 8 = 16
                                                                                            dy3 - dy2 = 72 - 24 = 48
                                                                                          dy4 - dy3 = 216 - 72 = 144
    We observe that the difference of differences of 2 consecutive y values are also not constant.
    Hence, the given function is not a quadratic function.
    c). Now, ratio between 2 consecutive y values-
                                                                                                  y subscript 2 over y subscript 1 = 12 over 4 = 3
                                                                                                  y subscript 3 over y subscript 2 = 36 over 12= 3
                                                                                                 y subscript 4 over y subscript 3 = 108 over 36 = 3
                                                                                                 y subscript 5 over y subscript 4 = 324 over 108 = 3
    We observe that difference between 2 consecutive y values is constant i.e. 3.
    Hence, the given function is an exponential function.
    Final Answer:-
    ∴ The given function is an exponential function.

    Related Questions to study

    General
    Maths-

    Solve the radical equation square root of 4 x plus 5 end root minus square root of x plus 1 end root equals 1 Check for extraneous solutions

    Solve the radical equation square root of 4 x plus 5 end root minus square root of x plus 1 end root equals 1 Check for extraneous solutions

    Maths-General
    General
    Maths-

    Solve the radical equation square root of 3 x minus 2 end root equals x minus 4

    Solve the radical equation square root of 3 x minus 2 end root equals x minus 4

    Maths-General
    General
    Maths-

    Does a linear , quadratic , or exponential function best model the data ? Explain.

    Does a linear , quadratic , or exponential function best model the data ? Explain.

    Maths-General
    parallel
    General
    Maths-

    The speed, v, of a vehicle in relation to its stopping distance, d, is represented by the equation v =3.57√d. What is the equation for stopping distance in terms of the vehicle’s speed?

    The speed, v, of a vehicle in relation to its stopping distance, d, is represented by the equation v =3.57√d. What is the equation for stopping distance in terms of the vehicle’s speed?

    Maths-General
    General
    Maths-

    Solve open parentheses x squared plus 4 x plus 5 close parentheses to the power of 3 over 2 end exponent plus 1 equals 0

    Solve open parentheses x squared plus 4 x plus 5 close parentheses to the power of 3 over 2 end exponent plus 1 equals 0

    Maths-General
    General
    Maths-

    The suspension cables from the Golden gate bridge’s towers are farther above the roadway near the towers and closer to the roadway near the middle of the bridge. You can figure out your distance from middle of the bridge, x, in feet, and height of the suspension cable, y, in feet, at your position by using the equation x = fraction numerator square root of y to the power of negative 220 end exponent end root over denominator 0.010583 end fractionAbout how far is the cable from roadway when you are 200 ft from middle of the bridge

    The suspension cables from the Golden gate bridge’s towers are farther above the roadway near the towers and closer to the roadway near the middle of the bridge. You can figure out your distance from middle of the bridge, x, in feet, and height of the suspension cable, y, in feet, at your position by using the equation x = fraction numerator square root of y to the power of negative 220 end exponent end root over denominator 0.010583 end fractionAbout how far is the cable from roadway when you are 200 ft from middle of the bridge