Question

In 1991, the moose population in a park was measured to be 3360. By 1996, the population was measured again to be 3560. If the population continues to change linearly:

Find a formula for the moose population, P, in terms of t, the
years since 1990. (I think my teacher meant for it to be 1991)
And what does your model predict for the moos population to be in 2007?

Answer 1

• P = 40t +3320
• 4000 in 2007

Explanation:

Given a moose population of 3360 in 1991 increases linearly to 3560 in 1996, you want a formula for the population P in terms of t, years since 1990, and you want the predicted population in 2007.

Slope

The slope of the linear function is given by ...

m = (y2 -y1)/(x2 -x1)

Here, we have (x, y) = (1, 3360) and (6, 3560). We calculate the slope to be ...

m = (3560 -3360)/(6 -1) = 200/5 = 40

Equation

The point-slope equation for the relation can be written as ...

y -k = m(x -h) . . . . . . . line with slope m through point (h, k)

y -3360 = 40(x -1) . . . . line with slope 40 through point (1, 3360)

y = 40x -40 +3360

y = 40x +3320 . . . . . . equation for population

Using the given variable definitions, we find the formula to be ...

P = 40t +3320 . . . . . formula for moose population

2007

Then the population in 2007 is predicted to be ...

P = 40(17) +3320 = 680 +3320 = 4000

The model predicts a moose population of 4000 in 2007.