Solve the problem.
-The population of a particular country was 22 million in 1984 ; in 1995, it was 34 million. The exponential growth function $\mathrm { A } = 22 \mathrm { e } ^ { \mathrm { kt } }$ describes the population of this country t years after 1984 . Use the fact that 11 years after 1984 the population increased by 12 million to find $\mathrm { k }$ to three decimal places.
A) $0.040$
B) $0.226$
C) $0.602$
D) $0.050$

Question

Quizplus · Accepted Answer

Let's use the given information to set up an equation that we can solve for k:
\begin{align*}
\mathrm{A}(0) &= 22\
\mathrm{A}(11) &= 34\
34 &= 22e^{11k}\
\frac{34}{22} &= e^{11k}\
\ln{\frac{34}{22}} &= 11k\
k &= \frac{\ln{\frac{34}{22}}}{11}\
k &\approx 0.040\ (\mathrm{to\ three\ decimal\ places})
\end{align*}

Therefore, the answer is choice A.

Solve the Problem A=22ekt\mathrm { A } = 22 \mathrm { e } ^ { \mathrm { kt } }A=22ekt

Solve the Problem $\mathrm { A } = 22 \mathrm { e } ^ { \mathrm { kt } }$