Linear Model for Population Growth

Question

In 1993, the moose population in a park was measured to be 3740. By 1996, the population was measured again to be 4430. If the population continues to change linearly

Find a formula for the moose population, , in terms of , the years since 1990.

  

 What does your model predict the moose population to be in 2006?  

Answer 1

We have the two points (3,3740) and (6,4430)

This being a linear model we now calculate the slope

I will use m for slope which is the annual rate of change for the moose population in the. park.

m = (4430 - 3740)/(6 - 3) = 690/3 = 230

Now we need to find the 'initial' moose population (the hypothetical moose population in 1990).

I will use slope-intercept method and use b to represent this value.

So P(t) = mt + b

3740 = 230(3) + b

solving gives us b = 3050

the equation is P(t) = (230)t + 3050

In the year 2006 t will be 16

So P(16) = (230)16 + 3050 = 6730

This model predicts that there will be 6730 moose in the park in the year 2006.