Question

Consider the scenario: A town’s population has been decreasing at a constant rate. In 2010 the population was 5800. By 2012 the population had dropped to 4,600. Assume the trend continues predict the population in 2016.

Answer 1

Given:

In 2010 the population was 5800.

2012 the population had dropped to 4,600.

Let 't=0' be the year 2010.

P(t) represents the year population of the town t years after 2010.

Slope of a function P(t) is

$\begin{gathered} m=\frac{4600-5800}{2012-2010} \\ m=-600 \end{gathered}$

Population of town t years after 2010.

$P(t)=-600(t)+5800$

Population in the year 2016 that is t=6

$\begin{gathered} P(6)=-600(6)+5800 \\ =2200 \end{gathered}$

Population in the year 2016 is 2200