Question

in 1993, the moose population in a park was measured to be 3020. by 1998, the population was measured again to be 2370. if the population continues to change linearly:
a.) find a formula for the moose population, $p$, in terms of $t$, the years since 1990.
$p(t)=$

b.) what does your model predict the moose population to be in 2008?

Explanation:

Step1: Determine two points

In 1993 ($t = 3$), $P(3)=3020$; in 1998 ($t = 8$), $P(8)=2370$. So we have two points $(3,3020)$ and $(8,2370)$.

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $m=\frac{P(8)-P(3)}{8 - 3}=\frac{2370 - 3020}{5}=\frac{- 650}{5}=-130$.

Step3: Use the point - slope form to find the equation

The point - slope form is $y - y_1=m(x - x_1)$. Using the point $(3,3020)$ and $m=-130$, we get $P - 3020=-130(t - 3)$.
Expand the right - hand side: $P-3020=-130t + 390$.
Then $P(t)=-130t+3410$.

Step4: Predict the population in 2008

In 2008, $t = 18$.
Substitute $t = 18$ into $P(t)=-130t + 3410$.
$P(18)=-130\times18+3410=-2340 + 3410 = 1070$.

Answer:

A. $P(t)=-130t + 3410$
B. $1070$