Question

The population of a town was 72 thousand in 2010, and has been growing by 8% each year. When will the population reach 160 thousand if the trend continues? Give at least 1 decimal place.

Answer 1

`10.4\ years`

Explanation:

In this problem we have a exponential function of the form

`y=a(b)^(x)`

where

y is the population of a town

x is the number of years since 2010

a is the initial value

b is the base

`a=72,000\ people`

`b=1+0.08=1.08`

substitute

`y=72,000(1.08)^(x)`

For
`y=160,000\ people`

substitute in the equation and solve for x

`160,000=72,000(1.08)^(x)`

`(160/72)=(1.08)^(x)`

Apply log both sides

`log(160/72)=(x)log(1.08)`

`x=log(160/72)/log(1.08)`

`x=10.4\ years`