In 1992, the moose population in a park was measured to be 3020. By 1996, the population was measured again to be 2540. If the population continues to change linearly: Find a formula for the moose population, P, in terms of t, the years since 1990. P(t): %3D What does your model predict the moose population to be in 2007?

It is given that, the population of moose in 1992 is 3020 and the population in 1996 is 2540.

Let t = 0 represent the year 1990 and P(t) represent the population of moose t years after 1990.

Let the formula for the moose population, in terms of t , the years since 1990  is $P\left(t\right)=at+b$.

Then, the slope of the function P(t) is,

$\begin{array}{rcl}\frac{2540-3020}{1996-1992}& =& -\frac{480}{4}\\ & =& -120\end{array}$

That is, $\begin{array}{rcl}a& =& -120\end{array}$.

Substitute $\begin{array}{rcl}a& =& -120\end{array}$ and t =2 in $P\left(t\right)=at+b$.

$$\begin{gathered} P\left(2\right)=-120\left(2\right)+b \\ b=3020+240=b \\ b=3260 \end{gathered}$$

Substitute $\begin{array}{rcl}a& =& -120\end{array}$ and b =3260 in $P\left(t\right)=at+b$.

$P\left(t\right)=-120t+3260$

Hence, the population of moose t years after 1990 is, $P\left(t\right)=-120t+3260$.