It is projected that t years from now the population of a city will be changing at the rate of $t ^ { 2 } e ^ { 0.01 t }$ thousand people per year. If the current population is 1 million, what will the population be 4 years from now?
A) 1,028,000
B) 1,000,022
C) 1,028,800
D) 1,021,984

Question

Quizplus · Accepted Answer

To find the population 4 years from now, integrate the rate of change function $t^2 e^{0.01t}$ from 0 to 4, and add the result to the current population of 1,000,000. The integral evaluates to approximately 21.984, so the population will be 1,021,984.

It Is Projected That T Years from Now the Population t2e0.01tt ^ { 2 } e ^ { 0.01 t }t2e0.01t

It Is Projected That T Years from Now the Population $t ^ { 2 } e ^ { 0.01 t }$