Chapter 4.6, Problem 7E

a.

To determine

Find the projected population for the year $2020$ for the following conditions.

Answer to Problem 7E

  $\boxed{233}$

Explanation of Solution

Given information:

The population of a country has a relative growth rate of $3\%$ per year. The government is trying to reduce the growth rate to $2\%$ . The population in $1995$ was approximately $110$ million. Find the projected population for the year $2020$ for the following conditions.

The relative growth rate remains at $3\%$ per year.

Calculation:

Consider exponentially growth model,

Initial population in $1995=110million$

Initial growth rate $r=3\%$

  $n\left(t\right)=n_0{e}^{rt}$

  $n\left(t\right)=110e^{0.03t}$

  $\begin{array}{l}now,\\ t=2020-1995=25\\ put,t=25\\ n\left(25\right)=110e^{0.03\left(25\right)}\\ n\left(25\right)=232.87\\ \approx 233\end{array}$

Hence, the solution is, $\boxed{233}$

b.

To determine

Find the projected population for the year $2020$ for the following conditions.

Answer to Problem 7E

  $\boxed{181.4}$

Explanation of Solution

Given information:

The population of a country has a relative growth rate of $3\%$ per year. The government is trying to reduce the growth rate to $2\%$ . The population in $1995$ was approximately $110$ million. Find the projected population for the year $2020$ for the following conditions.

The relative growth rate is reduced to 2% per year.

Calculation:

Consider exponentially growth model,

  $\begin{array}{l}n\left(t\right)=n_0{e}^{rt}\\ r=2\%=0.02\\ now,\\ t=2020-1995=25\\ put,t=25\\ n\left(25\right)=110e^{0.02\left(25\right)}\\ n\left(25\right)=181.3593\\ \approx 181.4\end{array}$

Hence, the solution is, $\boxed{181.4}$