Choose the one alternative that best completes the statement or answers the question.
-The population of a particular country was 30 million in 1984; in 1995, it was 34 million. The exponential growth function describes the population of this country t years after 1984. Use the fact that 11 years $$\mathrm { A } = 30 \mathrm { e } ^ { \mathrm { kt } }$$ after 1984 the population increased by 4 million to find k to three decimal places.
A) 0.126
B) 0.011
C) 0.630
D) 0.021

Question

Quizplus · Accepted Answer

To find the value of $k$, we use the given exponential growth function $A = 30e^{kt}$, where $A$ is the population in millions at time $t$ years after 1984, and $k$ is the growth rate. Given that 11 years after 1984 (i.e., $t = 11$), the population is 34 million, we can set up the equation $34 = 30e^{11k}$. Solving for $k$, we get $k \approx 0.011$.

Choose the One Alternative That Best Completes the Statement or Answers