Solve the problem.
-The population of a particular country was 30 million in 1984; in 1995, it was 34 million. The exponential growth function $\mathrm { A } = 30 \mathrm { e } ^ { \mathrm { kt } }$ describes the population of this country t years after 1984. Use the fact that 11 years
After 1984 the population increased by 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 $k$, substitute $A = 34$ (population in 1995), $t = 11$ (years after 1984), and the initial population $30$ into the equation $A = 30e^{kt}$. This gives $34 = 30e^{11k}$. Solving for $k$ involves dividing both sides by 30, getting $34/30 = e^{11k}$, and then taking the natural logarithm of both sides. The calculation yields $k \approx 0.011$.

Solve the Problem A=30ekt\mathrm { A } = 30 \mathrm { e } ^ { \mathrm { kt } }A=30ekt

Solve the Problem $\mathrm { A } = 30 \mathrm { e } ^ { \mathrm { kt } }$