A study indicates that x months from now the population of a certain city will be increasing at the rate of $( 3 + 4 x ) x ^ { - 1 / 2 }$ people per month. By how much will the population increase over the next 9 months?
A) 70 people
B) 80 people
C) 90 people
D) 100 people

Question

Quizplus · Accepted Answer

To find the total population increase over the next 9 months, integrate the rate function $(3 + 4x)x^{-1/2}$ from 0 to 9. The integral evaluates to 90, indicating the population will increase by 90 people.

A Study Indicates That X Months from Now the Population (3+4x)x−1/2( 3 + 4 x ) x ^ { - 1 / 2 }(3+4x)x−1/2

A Study Indicates That X Months from Now the Population $( 3 + 4 x ) x ^ { - 1 / 2 }$