Chapter 7.5, Problem 1QQ

To determine

To find multiple choice. And the number of acres will be consumed when t = 8.

Answer to Problem 1QQ

4.066 acres will be consumed when t = 8. Option (C).

Explanation of Solution

Given information: There are 2 acres consumed when t = 1 and 3 acres consumed when t = 5,

(A) 3.750

(B) 4.000

(C) 4.066

(D) 4.132

(E) 4.600

Calculation: The required solution is obtained as,

According to question,

Using the law of Exponential change, $y=y_0{e}^{kt}$ . The time would be from 1 to 5, t = 4.

  $\begin{array}{l}3=2e^{k\left(4\right)}\\ \ln \left(\frac{3}{2}\right)=k\left(4\right)\\ k=\frac{1}{4}\ln \left(\frac{3}{2}\right)\end{array}$

Plug in value for k into $y=y_0{e}^{kt}$ and with the new time limit from 5 to 8, t = 3.

  $3e^{\frac{3}{4}\ln \left(\frac{3}{2}\right)}=4.066$

Hence, 4.066 acres will be consumed when t = 8. Option (C).