Question

The function p(d) = 714(0.75)models the population of a town, in thousands,as a function of the number of decades since 2010. Which of the followingfunctions can be used to predict the population as a function of the number ofyears, x, since 2010?

Answer 1

We are given

`p(d)=714(0.75)^d`

where d is in decades

To write in terms of x, where x is in years

The scales factor between decades and years is 10

Thus, the scale factor will change

`d=10x`

To write in terms of x, we will have

`\begin{gathered} p(d)=714(0.75)^d \\ p(x)=714(0.75)^{(1)/(10)x} \\ p(x)=714(\sqrt[10]{0.75})^x \\ p(x)=714(0.9716416579)^x \\ p(x)=714(0.9716)^x \end{gathered}`

Therefore,

`p(x)=714(0.9716)^x`

Option C