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In 1992, the moose population in a park was measured to be 4280

In 1992, the moose population in a park was measured to be 4620. By 1996, the population was measured again to be 4020. 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)=

What does your model predict the moose population to be in 2002?

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2 Answers

Let t = the number of years since 1992. Let k = the linear coefficient. 

In 1992, we can represent the population as P=4620 + kt = 4620 + k(0) = 4620 (but we knew that). We can then use P=4620 + kt for our 1996 population:

P=4620 + k(4) = 4020

4k = 4020 - 4620 = -600

4k = -600

k = -150

So our equation is P = 4620 - 150t. 

I'll leave it to the student to determine the 2002 population. 

Was the 1992 moose population 4280 or 4620?  This will make a big difference in the slope and intercept of your equation and the expected value for 2002.

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