The population of deer in a forest has been increasing by 3 percent every 2 months. The population at the beginning of 2020 was estimated to be 325. If \(P\) represents the population of deer \(t\) years after 2020, which of the following equations gives the population of deer over time?

Summary Submit

Since the population is increasing by a percentage rather than a fixed amount, the equation must be exponential. The first two linear equations are not suitable for the situation.

We expect the deer to increase by 3% after 2 months, which is the same as \(\dfrac{1}{6}\) of a year. The exponential mode that reflects this is:

$$ P=325(1.03)^{6t} $$

When \(t=\frac{1}{6}\),

$$ P=325(1.03)^{6(\frac{1}{6})} $$ $$ P=325(1.03)^1 $$ $$ P=325(1.03) $$