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

Solution

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

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

Therefore,

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

Option C