Question

The population of Augusta, WI, had a population of 1253 in 2000. If the population increased by 3% each year, what would be the population of Augusta in 2016?

Answer 1

A=1,253×1.03^(16)
A=2,010.7

Answer 2

The Population growth function is given by:

`A(t) = A_0(1+r)^t`

where

`A_0` is the initial population.

r is the growth rate (in decimal)

t is the time in year.

As per the statement:

The population of Augusta, WI, had a population of 1253 in 2000.

In 2000

⇒
`A_0 =1253`

It is also given that the population increased by 3% each year

⇒r = 3% = 0.03

then;

`A(t) =1253(1+0.03)^t` .....[1]

We have to find the population of Augusta in 2016.

⇒t = 16 years

Substitute the given values in [1] we have;

`A(t) =1253(1+0.03)^(16)`

⇒
`A(t) =1253(1.03)^(16)`

⇒
`A(t) =1253 \cdot 1.60470644`

Simplify:

A(t) = 2,010.69717

Therefore, the population of Augusta in 2016 is, 2,010.7