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

Solution:

Given:

$\begin{gathered} P_o=1627 \\ r=6.8\text{ \%}=\frac{6.8}{100}=0.068 \end{gathered}$

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:

$\begin{gathered} when\text{ }t=8.5years \\ \\ Then, \\ P=1627e^{0.068\times8.5} \\ P=1627e^{0.578} \\ P=2900.08 \\ \\ Since\text{ the population must be a whole number,} \\ P=2900 \end{gathered}$