Question

In 2001, the moose population in a park was measured to be 4,850. By 2009, the population was measured again and was found to be 5,890. Assume the population continues to change linearly.

(a) Find a formula for the moose population, P, since 2001. (Let t represent the number of years since 2001.)

b) What does your model predict the moose population to be in 2017?
moose

Answer 1

Step-by-step explanation:

Letting 2001 equate to t=0 for our starting point

We started at (0, 4840) and 8 years later we are at (8, 6200)

4840 + 8t = 6200 The population went from 4840 to 6200 over 8 years.

Subtract 4840 from both sides

8t = 6200 - 4840

8t = 1360

divide both sides by 8 to isolate t

t = 1360/8

t = 170

The population rises by 170 moose per year

P(t) = 170t + 4840

b) In 2020... t = 2020 - 2001 = 19 years

P(t) = 170t + 4840

P(t) = 170(19) + 4840

P(t) = 8070

By our linear model there should be approximately 8070 moose by 2020.

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You could also take the two initial points (0, 4840), (8, 6200)

and find the slope m to set up the equation in

slope intercept form y = mt + b

where m is the slope and the point (0,b) = (0, 4840) is y-intercept.

m = (rise/run) = (6200-4840)/(8-0) = 170

y(t) = mt + b = 170t + 4840

There is another, probably easier, way to find the "245" for this

problem. We have two points (0, 4240) and (8, 6200)

We can use that to find the slope of our equation to set up the

equation in slope intercept form of y = mx + b... or, in this case

y = mt + b since y is a function of t

m = slope of the line, and the point (0,b) is the y-intercept = (0, 4240)

m = (change in y)/(change in t) = (6200-4240)/(8-0) = 1960/8 = 245

We can then set up our equation y = mt + b

using 245 for m, and 4240 for b

y = 245t + 4240