Question

In 1992, the moose population in a park was measured to be 4260. By 1996, the population was measured again to be 3660. 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 2008?

Answer 1

In 1992, the moose population in a park was measured to be 4260. By 1996, the population was measured again to be 3660. 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 2008?

Answer:

Model predict the moose population to be in 2008 is 1860

Solution:

Let us consider this problem on graph, taking the x axis to be years since 1990 and y on the graph be the number of moose

We have two points on the graph: (2, 4260) and (6, 3660)

Using the slope formula we can find the slope :

`\mathrm{m}=(y_(2)-y_(1))/(x_(2)-x_(1))`

`m=((3660-4260))/((6-2))`

m = -150

Now that we have the slope of the line, we can use the point-slope formula to find the equation for the line as follows:-

`\begin{array}{l}{y-y_(1)=m\left(x-x_(1)\right)} \\\\ {y-4260=-150(x-2)} \\\\ {y-4260=-150 x+300} \\\\ {y=-150 x+4560}\end{array}`

Since the formula that is being sought is supposed to be interms of P and t, we will replace y with P and x with t

P(t) = -150t + 4560

Number of years from 1990 to 2008 is

2008 - 1990 = 18

So, population in 2008 will be

P(18) = -150 (18) + 4560

P(18) = -2700 + 4560

P(18) = 1860

Thus the model to predict the moose population in 2008 is found