A study indicates that x months from now the population of a certain city will be increasing at the rate of $( 8 + 15 x ) x ^ { - 1 / 2 }$ people per month. By how much will the population increase over the next 16 months?
A) 704 people
B) 714 people
C) 694 people
D) 640 people

Question

Quizplus · Accepted Answer

To find the total increase in population over the next 16 months, integrate the rate function $(8 + 15x)x^{-1/2}$ from 0 to 16. The integral evaluates to 704.

A Study Indicates That X Months from Now the Population (8+15x)x−1/2( 8 + 15 x ) x ^ { - 1 / 2 }(8+15x)x−1/2

A Study Indicates That X Months from Now the Population $( 8 + 15 x ) x ^ { - 1 / 2 }$