The fox population in a certain region has a continuous growth rate of 6 percent per year. It is estimated that the population in the year 2000 was 18900.

Calculation:

The general form of an exponential equation is,

\(\displaystyle{P}{\left({t}\right)}={P}_{{0}}{e}^{{{r}{t}}}\)

Here, \(\displaystyle{P}_{{0}}={18900}\)

\(\displaystyle{r}={6}\%={\frac{{{6}}}{{{100}}}}={0.06}\)

a) Therefore, a function that models the population t years after 2000 is

\(\displaystyle{P}{\left({t}\right)}={18900}{e}^{{{0.06}{t}}}\)

b) For 2000, t=0

Therefore for 2008, t=8

Therefore, the estimation of fox population in the year 2008 is

\(\displaystyle{P}{\left({8}\right)}={18900}{e}^{{{0.06}{\left({8}\right)}}}\)

\(\displaystyle{P}{\left({8}\right)}\approx{30544}\)

Calculation:

The general form of an exponential equation is,

\(\displaystyle{P}{\left({t}\right)}={P}_{{0}}{e}^{{{r}{t}}}\)

Here, \(\displaystyle{P}_{{0}}={18900}\)

\(\displaystyle{r}={6}\%={\frac{{{6}}}{{{100}}}}={0.06}\)

a) Therefore, a function that models the population t years after 2000 is

\(\displaystyle{P}{\left({t}\right)}={18900}{e}^{{{0.06}{t}}}\)

b) For 2000, t=0

Therefore for 2008, t=8

Therefore, the estimation of fox population in the year 2008 is

\(\displaystyle{P}{\left({8}\right)}={18900}{e}^{{{0.06}{\left({8}\right)}}}\)

\(\displaystyle{P}{\left({8}\right)}\approx{30544}\)