Question

The population of a small town in central Florida has shown a linear decline in the years 1994-2004. In 1994 the population was 31900 people. In 2004 it was 28700 people.

Answer 1

Given:

$\begin{gathered} \text{When t=0, }P(0)=31900 \\ \text{When t=}10\text{ ; P(10)=}28700 \end{gathered}$

A)

Year is calculated from 1994 as zero, 1995 as 1, 1996 as 2 and so on.

$\begin{gathered} \frac{P(t)-31900}{28700-31900}=\frac{t-0}{10-0} \\ \frac{P(t)-31900}{-320}=t \\ P(t)-31900=-320t \\ P(t)=31900-320t \end{gathered}$

B)

year 2007 is taken as t=13

$\begin{gathered} P(13)=31900-320(13) \\ P(13)=31900-4160 \\ P(13)=27740 \end{gathered}$