Question

Suppose a city with population 100,000 has been growing at a rate of 8​% per year. If this rate​ continues, find the population of this city in 17 years.

Answer 1

`370,002\ people`

Explanation:

In this problem we have a exponential equation of the form

`y=a(b^x)`

where

y is the population of the city

x is the number of years

a is the initial value or y-intercept

b is the base

r is the rate of growth

b=(1+r)

we have

`a=100,000\ people\\r=8\%=8/100=0.08\\b=1+0.08=1.08`

substitute

`y=100,000(1.08^x)`

For x=17 years

substitute the value of x in the exponential equation and solve for y

`y=100,000(1.08^17)`

`y=370,002\ people`