Solve.
-The population of a particular country was 23 million in 1980 ; in 1990 , it was 34 million. The exponential growth function $\mathrm { A } = 23 \mathrm { e } ^ { \mathrm { kt } }$ describes the population of this country t years after 1980 . Use the fact that 10 years after 1980 the population increased by 11 million to find $\mathrm { k }$ to three decimal places.
A) $0.039$
B) $0.240$
C) $0.666$
D) $0.049$

Question

Quizplus · Accepted Answer

To find $k$, use the given exponential growth function $A = 23e^{kt}$ with $A = 34$ million (population in 1990) and $t = 10$ years (from 1980 to 1990). Substituting these values gives $34 = 23e^{10k}$. Solving for $k$ involves dividing both sides by 23, getting $34/23 = e^{10k}$, and then taking the natural logarithm of both sides. This results in $ln(34/23) = 10k$, and solving for $k$ gives $k = \frac{ln(34/23)}{10}$, which approximately equals $0.039$.

Solve -The Population of a Particular Country Was 23 Million A=23ekt\mathrm { A } = 23 \mathrm { e } ^ { \mathrm { kt } }A=23ekt

Solve
-The Population of a Particular Country Was 23 Million $\mathrm { A } = 23 \mathrm { e } ^ { \mathrm { kt } }$