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.

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

[tex]t=2,P=3570\\t=9,P=3640[/tex]

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

[tex]P=mt+b[/tex]

The slope [tex]m[/tex] is

[tex]m=\frac{3640-3570}{9-2} =10[/tex]

therefore we have

[tex]P=10t+b[/tex]

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

[tex]3570=10(2)+b[/tex]

[tex]b=3550[/tex]

With this value of [tex]b[/tex], we finally have the formula for the moose population:

[tex]\boxed{P=10t+3550}[/tex]

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.

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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.