Find a formula for the moose population, P , in terms of t , the years since 1990.

Question

In 1994, the moose population in a park was measured to be 4520. By 1997, the population was measured again to be 5270. If the population continues to change linearly:

Find a formula for the moose population,

P, in terms of

t, the years since 1990.

What does your model predict the moose population to be in 2004?

Answer 1

For this question, the x-axis represents the years since 1990, and the y-axis represents the moose population. The problem therefore gives us two points on our population line: (4, 4520) and (7, 5270). From two points, we know how to get the slope of a line: (y2 - y1) / (x2 - x1), or (5270-4520)/(7-4), which equals (750/3), or 250. Therefore, P = 250t + b, where b is the intercept of the line.

We solve for the intercept of the line by plugging in one of the points we already know. Let's do (4, 4520). Therefore, 4520 = 250(4) + b. Simplifying, 4520 = 1000 + b, so b = 3520. The equation of our line is P = 250t + 3520.

To predict the moose population in 2004, we just plug that t-coordinate (which is 2004-1990, or 14), into our equation! P = 250(14) + 3520, which solves to P = 7,020. That is the predicted moose population in 2004!