Question

in 1991, the moose population in a park was measured to be 4500. By 1996, the population was measured again to be 5900. If the population continues to change linearly.Find a formula for the moose population, P, in terms of t, the years since 1990.what does your model predict the moose population to be in 2006?

Answer 1

The formula is P(t) = 280t + 4220

In 2006 the population will be 8700

Step-by-step explanation

If the population changes linearly, we're looking for a formula like:

`P(t)=mt+P_0`

P0 is the initial population, in 1990. m is the slope and t is the time in years since 1990.

We have two points (t, P(t)):

• (1, 4500) --> 1 year after 1990 the population was 4500

,

• (6, 5900) --> 6 years after 1990 the population was 5900.

With this information we can find the slope m:

`m=(\Delta P)/(\Delta t)=(5900-4500)/(6-1)=(1400)/(5)=280`

The slope is 280. For now, the formula is:

`P(t)=280t+P_0`

To find the y-intercept P0, we have to use one of the points. Using the first point (1, 4500) replace P(t) = 4500 and t = 1 and solve for P0:

`\begin{gathered} 4500=280+P_0 \\ P_0=4500-280 \\ P_0=4220 \end{gathered}`

The formula is:

`P(t)=280t+4220`

To find the population in 2006 we have to know how many years after 1990 is 2006:

`2006-1990=16`

We have to replace t = 16 in our formula:

`\begin{gathered} P(16)=280\cdot16+4220 \\ P(16)=8700 \end{gathered}`