Chapter 8, Problem 2STP

To determine

To find: The correct option for the time to reach the population of 3000.

Answer to Problem 2STP

The correct option is G

Explanation of Solution

Given:

The number of birds are 3500.

The rate of decrease in population is $5\%$ .

The given logarithm function is $t={\log }_{0.95}\frac{p}{3500}$ .

Calculation:

Consider the expression for the time is,

  $t={\log }_{0.95}\frac{p}{3500}$

Then, the time taken to reach the bird population to 3000 is,

  $\begin{array}{l}t={\log }_{0.95}\frac{3000}{3500}\\ {0.95}^t=0.857\\ \ln {0.95}^t=\ln 0.857\\ t\ln 0.95=\ln 0.857\end{array}$

Solve further as,

  $\begin{array}{c}t=\frac{-0.154}{-0.051}\\ =3.02\end{array}$