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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.

1 Answer

2 votes

Solution:

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}
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