Chapter 8.6, Problem 40PPS

(a).

To determine

To find: The average annual rate of growth in the population if the grizzly bears reproduce once a year.

Answer to Problem 40PPS

The annual growth rate grizzly bear population is $7.69\%$ .

Explanation of Solution

Given information:

Thegrizzly bears population in certain nation park

  $\begin{array}{l}5\text{years}\text{age}=325\\ \text{Today}=450\end{array}$

Calculation:

Consider the grizzly bears population in certain nation park

  $\begin{array}{c}5\text{years}\text{age}=325\\ \text{Today}=450\end{array}$

Consider annual growth rate for $n$ years is:

  $\text{Rate}=\frac{1}{n}\left(\frac{V_{present}-V_{past}}{V_{past}}\right)\times 100$

Therefore, the annual growth rate grizzly bear population is:

  $\begin{array}{c}\text{Rate}=\frac{1}{5}\left(\frac{450-325}{325}\right)\times 100\\ =7.69\%\end{array}$

Therefore, the annual growth rate grizzly bear population is

  $7.69\%$ .

(b).

To determine

To find: The in how many years it will take to reach the maximum population if the population growth continues at the same average rate.

Answer to Problem 40PPS

The number of pet owners in the year $2010$ is approximately $62.737$ thousand.

Explanation of Solution

Given information:

The grizzly bears population in certain nation park

  $\begin{array}{l}5\text{years}\text{age}=325\\ \text{Today}=450\end{array}$

Calculation:

Consider $n$ number of years needed form the current day to reach the maximum population that is $750$ ,Consider

  $V_{present}=V_{past}+\frac{n\times Rate\times V_{past}}{100}$

Therefore:

  $\begin{array}{c}750=450+\frac{n\times 7.69\times 450}{100}\\ 34.61n=300\\ n=\frac{300}{34.61}\\ \approx 9\end{array}$

Therefore $9$ years needed for the current day to reach the maximum population.