For the exponential function represented in the table below

For the exponential function represented in the table below, determine the initial value, the n-unit growth factors, and the exponential function that models the data.

initial amount= 84

a.) The 1-unit growth factor:

b) The 1-unit percent change:

c.) The 6-unit growth factor:

d.) The 1/3-unit growth factor:

e.) Function definition:

Solution

Let us assume that f(x) = ab^x

then 84 = ab⁰

=> a = 84

and 109.17 = ab²

=> 109.17 = 84(b)²

=> b = 1.14

this is the 1 unit growth factor.

b] 1 unit % change is: (1.14(84) - 84)/84 x 100 = 14%.

d] 6 unit growth factor : 1.14⁶ = 2.195

e] 1/3 unit growth factor: b^1/4 = (1.14)^1/3 = 1.0446

d] f(x) = 84(1.14)^x