What does your model predict the moose population to be in 2007?

Question

In 1995, the moose population in a park was measured to be 8600. By 1999, the population was measured again to be 8900. If the population continues to change linearly, find an equation for the moose population, , as a function of , the years since 1989. 

Answer 1

Hi Kassandra P.,

I find it helpful to plot a graph to help visualize what is going on. Since this is a linear function it should be fairly easy to plot.

I made the x-axis the time t-axis, and the y-axis the P(t)-axis. Since were starting at the year 1989, from (0, 0), I went over 6 units on the t-axis (1995 - 1989 = 6) and made a mark, then 4 units more units to 10 (1999 -1989 = 10). Then I went up a distance on the P(x)-axis and made a mark for 8600 and slightly above and made another mark for 8900. Two points (6, 8600) and (10, 8900) make a straight line (linear). With those two points we can create a linear equation.

m = (8900 - 8600) / (10 - 6) = 75

P(t) - 8600 = 75(t - 6)

P(t) = 75t + 8150

Now since we started at 0 for year 1989, we can say (t) is the Year of population desired Y(t) minus 1989 or t = [Y(t) - 1989] to put the equation as a function of the year you input.

P(t) = 75[Y(t) - 1989] + 8150

When Y(t) = 2007:

P(t) = 75[(2007-1989) + 8150

P(t) = 75(18) + 8150

P(t) = 9500, moose in 2007.

I hope this helps, Joe.