Dale P. answered • 03/14/21
Approachable Chemistry Doctorate Willing to Move at Your Pace
So first lets set up what we need. We need to find an equation that finds the Moose population (P) as a function of the year (t). They want a linear equation so we need to fit it to the formula y=mx+b.
First question is what are y and x?
well y needs to depend on x. In the problem we're told that we want to find the Moose population as it changes with the year. So that would make Moose population (P) the y coordinate and the year (t) as the x axis.
Before we start let's do one more thing. The question asks us to find the equation for the years past 1990. That means we need to shift our 0 to 1990. To do this we subtract 1990 from any year so 1992 becomes (1992-1990) 2 and 1999 becomes 9.
Now we need to solve for the equation. For the equation we need two constants m and b. Two find two constants we need two equations. Can we make two?... Yes. We have two years and two populations so we have, with the adjusted years, the following:equations. I have also switched x and y with t and P.
P = mt + b
5000 = 2m + b
2800 = 9m + b
First we solve one equation for b in terms of m so we can substitute in the second equation and solve for m. I chose to solve for b because it was simpler. You can solve for either.it should give the same result in the end. I'll solve the top equation. You can check me with the second if you would like extra practice.
b=5000-2m
2800 = 9m + (5000-2m) - substitute for m in second equation
-2200 = 7m - combine like terms
m = -2200/7 - solve for m
With the solved m you can plug it into either equation to find b. I'll use the top equation again.
5000 = 2(-2200/7) + b
35000 = -4400 + 7b - multiply by 7 to make math easier to follow for me (not necessary)
39400 = 7b - combine like terms
39400/7 = b - solve for b
With this we have the equation P = (-2200/7)t+ 39400/7 With that you can solve for the year 2003. Which would be t = 2003 - 1990 remember!
Let me know if you have any questions,
Dale
