Question

In 1992, the moose population in a park was measured to be 3570. By 1999, the population was measured again to be 3640. If the population continues to change linearly:
Find a formula for the moose population,
,P, in terms of ,t, the years since 1990.

Answer 1

Answer:

The formula for the moose population is

$P=10t+3550$

Step-by-step explanation:

In 1992—that is, 2 years after 1990 or at $t=2$—the population $P$ is 3570, and in 1999 ($t=9$) population is 3640; so we have

$t=2,P=3570\\t=9,P=3640$

Now the formula that will model the moose population will be of the form:

$P=mt+b$

The slope $m$ is

$m=\frac{3640-3570}{9-2} =10$

therefore we have

$P=10t+b$

Now we know that at $t=2,$ $P=3570$, so we put these values in and solve for $b:$

$3570=10(2)+b$

$b=3550$

With this value of $b$, we finally have the formula for the moose population:

$\boxed{P=10t+3550}$