Question

The initial population of the town was estimated to be 12,500 in 2005. The population has increased by about 5.4% per year since 2005.

Formulate the equation that gives the population, A(x) , of the town x years since 2005. If necessary, round your answer to the nearest thousandth.

A(x)=__(_)^x

Answer 1

`A(x) = 12500(1.054)^x`

Explanation:

Exponential equation for population growth:

Considering a constant growth rate, the population, in x years after 2005, is given by:

`A(x) = A(0)(1 + r)^x`

In which A(0) is the population in 2005 and r is the growth rate, as a decimal.

The initial population of the town was estimated to be 12,500 in 2005.

This means that
`A(0) = 12500`

The population has increased by about 5.4% per year since 2005.

This means that
`r = 0.054`

So

`A(x) = A(0)(1 + r)^x`

`A(x) = 12500(1 + 0.054)^x`

`A(x) = 12500(1.054)^x`