Question

A town’s population increases at a constant rate. In 2010 the population was 55,000. By 2012 the population had increased to 76,000. If this trend continues, predict the population in 2016. what will the population be in 2016

Answer 1

Given:

A town’s population increases at a constant rate.

Let the equation of the population is as follows:

`y=a(r)^x`

where: (y) is the population after x years from 2010, and (r) is the rate of increase

In 2010 the population was 55,000

So, x = 0, y = 55,000

so, the value of a = 55,000

By 2012 the population had increased to 76,000

so, x = 2012 - 2010 = 2, y = 76,000

So, substitute (x) and (y) and (a) to find the value of (r)

`\begin{gathered} 76000=55000(r)^2 \\ r^2=(76000)/(5000)\approx1.3818 \\ r=√(1.3818)\approx1.1755 \end{gathered}`

So, the equation of the population will be as follows:

`y=55000(1.1755)^x`

now, we will predict the population in 2016

So, x = 2016 - 2010 = 6

So, the value of y will be as follows:

`y=55000(1.1755)^6=145,116`

So, the answer will be:

The population will be in 2016 = 145,116