precalculus help

Question

In 1994, the moose population in a park was measured to be 4450. By 1997, the population was measured again to be 4420. If the population continues to change linearly:

A.) Find a formula for the moose population,  p, in terms of t, the years since 1990.

p(t)=   

B.) What does your model predict the moose population to be in 2009?

Answer 1

Since the population is growing linearly, we can model the moose population using a linear equation in the form y=mx+b.

(a)

From the problem, we identify the points (1994, 4450) and (1997, 4420). Now, all we need to do is find the equation of the line connecting them.

I'm going to start with finding the slope:

m = (4420 - 4450) / (1997 - 1994) = -10

Sadly, the population is dropping at a rate of 10 meese per year.

Now let's solve for b to complete the equation. I'm going to plug in a slope of (-10) and the point (1994, 4450) to solve for b:

y = mx + b

(4450) = (-10)(1994) + b

24390 = b

putting it all together:

p(t) = -10t + 24390

(b)

to find population in 2009, plug in t=2009:

p(2009) = -10(2009) + 24390

p(2009) = 4300

population in 2009 = 4300

hope this helps!