Question

A town's population grows at a rate proportional to itspopulation. If the growth rate is 6.8% per year and thecurrent population is 1627, what will the population be8.5 years from now?a) Write the equationb) Determine the future population of the town.

Answer 1

Given:

`\begin{gathered} P_o=1627 \\ r=6.8\text{ \%}=(6.8)/(100)=0.068 \end{gathered}`

The equation of the population can be gotten using the formula;

`P=P_oe^(rt)`

Hence, the equation is:

`P=1627e^(0.068t)`

The population of the town 8.5years from now will be:

`\begin{gathered} when\text{ }t=8.5years \\ \\ Then, \\ P=1627e^(0.068*8.5) \\ P=1627e^(0.578) \\ P=2900.08 \\ \\ Since\text{ the population must be a whole number,} \\ P=2900 \end{gathered}`