We will consider x on the graph to be years since 1990 and y on the graph to be the number of Moose.
We have two points on the graph: (4, 4290) and (8, 3850)
Using the slope formula (m = [y_{2}  y_{1}]/[x_{2}  x_{1}]), we can find the slope of this line:
m = (y_{2}  y_{1})/(x_{2}  x_{1}) Slope formula
m = (3850  4290)/(8  4) Substitution
m = 440/4 Solve the subtraction problems in the parenthesis
m = 110 Reduce the fraction
Now that we have the slope of the line, we can use the pointslope formula (y  y_{1} = m[x  x_{1}]) to find the equation for the line. I will use the first point, but either point will produce the same answer.
y  y_{1} = m(x  x_{1}) Pointslop e formula
y  4290 = 110(x  4) Substitution
y  4290 = 110x + 440 Distribute the 110
y  4290 + 4290 = 110x + 440 + 4290 Add 4290 to each side
y = 110x + 4730 Simplify
Since the formula that is being sought is supposed to be interms of P and t, I will replace y with P and x with t.
P(t) = 110t + 4730
To predict the population in 2006, we need to determine the years from 1990 to 2006.
2006  1990 = 16
P(16) = 110 (16) + 4730
P(16) = 1760 + 4730
P(16) = 2970
2/13/2013

John R.