Question

In 2011, the population of a town was 55,000. If the population increases 3.1% annually, which equation best models the population?

Answer 1

Given, the initial population, Po=55000.

The rate of increase in population, R=3.1%.

Then, the population after x years can be given as,

$\begin{gathered} f(x)=P_0(1+\frac{R}{100})^x \\ f(x)=55000(1+\frac{3.1}{100})^x_{} \\ =55000(1+0.031)^x \\ f(x)=55000(1.031)^x \end{gathered}$

Therefore, the equation which models the population is,

$f(x)=55000(1.031)^x$