Question

The population in a certain city was 64,000 in 2000, and its future size is predicted to be P(t)=64,000e0.014t, where t is the number of years after 2000.Complete parts a through d below.

Answer 1

So,

Here we have the following function:

$P(t)=64000e^{0.014t}$

We want to know if the model indicates that the population is increasing or decreasing.

For this, if we graph, we would obtain something like:

So, the population is clearly increasing.

Suppose we want to know the population in 2002. So, remember that 2002 is two years after 2000, now we're going to replace t=2 in the equation:

$\begin{gathered} P(2)=64000e^{0.014(2)} \\ P(2)=64000e^{0.028} \\ P(2)=65817.32 \end{gathered}$

In 2020,

$\begin{gathered} P(20)=64000e^{0.28} \\ P(20)=84680 \end{gathered}$

The average rate of growth:

$\frac{64000e^{0.28}-64000e^0}{20-0}=\frac{84680-64000}{20}=1034$