Question

In 1993, the moose population in a park was measured to be 3030. By 1996, the population was measured again to be 2910. 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

To find a formula for the moose population, P, in terms of t, the years since 1990 (assuming the measurement in 1993 was taken in year 3 and the measurement in 1996 was taken in year 6), we can use linear regression with the two data points:

(3, 3030) and (6, 2910)

First, we need to find the slope (m) of the line that passes through these two points:

m = (2910 - 3030) / (6 - 3) = -40

Next, we can use the point-slope form of a linear equation:

y - y1 = m(x - x1), where (x1, y1) is a point on the line

We can choose either one of the two data points, but let's use (3, 3030):

P - 3030 = -40(t - 3)

Simplifying, we get:

P = -40t + 3150

Therefore, the formula for the moose population, P, in terms of t, the years since 1990, is:

P = -40t + 3150