Question

in 1991, the moose population in a park was measured to be 3880. by 1997, the population was measured again to be 4180. 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 2006?

question help: video

Explanation:

Step1: Determine two points

In 1991 ($t = 1$), $P(1)=3880$; in 1997 ($t = 7$), $P(7)=4180$.

Step2: Calculate the slope $m$

The slope formula is $m=\frac{P(7)-P(1)}{7 - 1}$. Substitute $P(1) = 3880$ and $P(7)=4180$ into it: $m=\frac{4180 - 3880}{7 - 1}=\frac{300}{6}=50$.

Step3: Find the y - intercept $b$

Use the point - slope form $P(t)=mt + b$ and the point $(1,3880)$. Substitute $t = 1$, $m = 50$ and $P(1)=3880$ into $P(t)=mt + b$: $3880=50\times1 + b$, then $b=3880 - 50=3830$.
So the formula is $P(t)=50t+3830$.

Step4: Predict the population in 2006

For 2006, $t=2006 - 1990=16$. Substitute $t = 16$ into $P(t)=50t + 3830$: $P(16)=50\times16+3830=800 + 3830=4630$.

Answer:

A. $P(t)=50t + 3830$
B. $4630$