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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, P, as a function of t, the years since 1989. 

1 Resposta

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.

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