Formula for linear growth is f(x) = mx+b

m is the slope or in this case the population growth/decline. x is the number of years and b is the original population.

in this case it will be p(t) = mt+b

lets find the population decline m.

In 1996 the population was 3200. This is a decline of 140 moose over 2 years. We need to know how many moose decline each year, so divide 140/2 and you get 70.

70 moose are declining each year. So m = 70, but it's declining so we need a negative. m = -70

So lets put it in the equation:

p(t) = -70t + b

So now it's easy to find b. We just plug in the year and population and get our b. Let's use 1996. The time has been 6 years from 1990 and the population in 1996 is 3200.

use the formula p(t) = -70(t) + b

t = 6

p(6) = 3200.

So p(6) = -70(6) + b = 3200

p(6) = -420 + b = 3200

-420 + b = 3200

b = 3620

Now you can plug in the years for t and get the decline in population.

We need the year 2009. So 2009-1990 = 19. Our t=19.

p(19) = -70(19) + 3620 = -1330 + 3620 = 2290.

## Comments

isn't 142,920 a little too high for the population in 1990?

Ralph,

142,920 is the population at t=0 AD (when we started time in years)

If you wanted to find out how many moose are there in the year 1990, you would need to perform the following calculation: 142920 - 70*1990 = 3620.

Let me know if you have any additional questions!

but the rest of us got 3620 for t(0) or population in 1990?

Ralph, I am not sure I understand your question. In 1990 the population is 3620 which would be t(1990) not t(0).

Let me know what you think.

Thanks,

Nandini

What I'm trying to say is that I used t=0 for 1990 so that each succeeding year from 1990 is t = 1, t =2, t=3, and so on. Since the problem stated: in terms of, "t", the years since 1990. P(t)= ????