Question

# 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 18

Exponential models
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.
(a) Find a function that models the population t years after 2000 (t=0 for 2000). Hint: Use an exponential function with base e.
(b) Use the function from part (a) to estimate the fox population in the year 2008.

2021-01-06
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
$$\displaystyle{P}{\left({8}\right)}={18900}{e}^{{{0.06}{\left({8}\right)}}}$$
$$\displaystyle{P}{\left({8}\right)}\approx{30544}$$