Question

In 1995, the moose population in a park was measured to be 7800. By 1997, the population wasmeasured again to be 8300. If the population continues to change linearly, find an equation for themoose population, P, as a function of t, the years since 1987.What does your model predict the moose population to be in 2003?

Answer 1

Given:

In 1995, the population is 7800.

In 1997 population is 8300.

it implies that population is increase by 500 after 2 years.

As ,the population continues to change linearly.

From 1987 to 1995 there are 8 years and from 1987 to 1997 10 years.

Note: here the x values are from the year 1987 and y values are population.

We have two points ( 8,7800) and (10,8300)

Slope of the equation is given by,

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ (x_1,y_1)=(8,7800) \\ \mleft(x_2,y_2\mright)=(10,8300) \\ m=(8300-7800)/(10-8) \\ m=250 \end{gathered}`

The slope -point form of equation of line is,

`\begin{gathered} y-y_1=m(x-x_1) \\ (x_1,y_1)=(8,7800) \\ y-7800=250(x-8) \\ y-7800=250x-2000 \\ y=250x+5800 \end{gathered}`

An equation for the moose population P as a function of t years since 1987 is,

P(t)=250t+5800.

The population in the year 2003 is,

Note: we need to determine the years from 1987 to 2003

2003-1987=16

So, the population in the year 2003 that means after 16 years from 1987.

`\begin{gathered} P(16)=250*16+5800 \\ P(16)=4000+5800 \\ P(16)=9800 \end{gathered}`

Answer:

1) An equation for the moose population P as a function of t years since 1987 is,

P(t)=250(t)+5800.

2) The population in the year 2003 is 9800.