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
ANSWERED
asked 2021-01-05
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.

Answers (1)

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
\(\displaystyle{P}{\left({8}\right)}={18900}{e}^{{{0.06}{\left({8}\right)}}}\)
\(\displaystyle{P}{\left({8}\right)}\approx{30544}\)
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