Solve the problem.
-The population of a country is modeled by the function $P ( t ) = 15.9 e ^ { 0.01462 t }$ where $P ( t )$ is the population (in millions) $t$ years after January 1, 2000. Use the model to predict the year during which year the population will reach 30 million if this trend continues.
A) 2,043
B) 2,014
C) 2,084
D) 2,004

Question

Quizplus · Accepted Answer

To find the year when the population will reach 30 million, set $P(t) = 30$ and solve for $t$:$$30 = 15.9e^{0.01462t}$$Divide both sides by 15.9:$$e^{0.01462t} = \frac{30}{15.9}$$Take the natural logarithm of both sides:$$0.01462t = \ln\left(\frac{30}{15.9}\right)$$Solve for $t$:$$t = \frac{\ln\left(\frac{30}{15.9}\right)}{0.01462}$$$$t \approx 43$$Since $t$ is the number of years after January 1, 2000, the year during which the population will reach 30 million is $2000 + 43 = 2043$.

Solve the Problem P(t)=15.9e0.01462tP ( t ) = 15.9 e ^ { 0.01462 t }P(t)=15.9e0.01462t

Solve the Problem $P ( t ) = 15.9 e ^ { 0.01462 t }$