For the exponential represented in the table below determine

For the exponential represented in the table below, determine the initial value, the n unit growth factors, and the exponential function that models the a. The initial value. b. The 1-unit growth factor c. The 1-unit percent change d. The -3 unit growth factor The 1-4 unit growth factor f. Function definition

Solution

table is as follows

x        f(x)

1        756.09

4        608.17

7        489.18

10      393.48

standard exponential formula is given by

P = Po e^rt

plugging the values from data into the equation

756.09 = Po e ^r --------------------- eq 1

608.17 = Po e^4r -------------------- eq 2

dividing the 2 equations

608.17 / 756.09 = e^3r

r = -.0725

Po = 608.17 / .74826 = 812.779

hence, initial value = 812.779

exponential model is P = 812.779 e^-.0725 x

percentage change = 7.25%

1 unit growth factor = - .0725