Solve the problem.
-A certain country's population $\mathrm { P } ( \mathrm { t } )$, in millions, $\mathrm { t }$ years after 1980 can be approximated by
$$\mathrm { P } ( \mathrm { t } ) = 3.495 ( 1.016 ) ^ { \mathrm { t } } \text {. }$$
In what year will the country's population reach 6 million?
A) About 2024
B) About 2019
C) About 2004
D) About 2014

Question

Quizplus · Accepted Answer

We need to solve the equation $3.495(1.016)^t = 6$.

Dividing both sides by $3.495$, we get $(1.016)^t \approx 1.717$.

Taking $\log$ of both sides, we get $t \log(1.016) \approx \log(1.717)$.

Solving for $t$, we get $t \approx \frac{\log(1.717)}{\log(1.016)} \approx 34.33$.

Adding 34.33 years to 1980, we get the year as approximately $2014$.

Therefore, the answer is $\boxed{	ext{(D)}}$.

Solve the Problem P(t)\mathrm { P } ( \mathrm { t } )P(t)

Solve the Problem $\mathrm { P } ( \mathrm { t } )$