Solve the problem.
-The population of a particular country was 22 million in 1985 ; in 2000 , it was 31 million. The exponential growth function $\mathrm { A } = 22 \mathrm { e } ^ { \mathrm { kt } }$ describes the population of this country t years after 1985 . Use the fact that 15 years after 1985 the population increased by 9 million to find $k$ to three decimal places.
A) $0.023$
B) $0.146$
C) $0.435$
D) $0.033$

Question

Quizplus · Accepted Answer

The population increased by 9 million in 15 years, so $A(15) - A(0) = 9$. Substituting into the given function, we get $22e^{15k} - 22 = 9$. Solving for $k$, we get $k = \frac{\ln(9/22)}{15} \approx 0.023$.

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

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