A mountain pine beetle population can double every year if conditions are ideal. Assume the forest in Jasper National Park,AB has a population of 20 000 beetles.

Question

A mountain pine beetle population can double every year if conditions are ideal. Assume the forest in Jasper National Park,AB has a population of 20 000 beetles. 
The formula P=20 000(2)^n can model the population,P,after n years.

a) How many beetles were there in the forest four years ago? Eight years ago?

b) If the conditions remain ideal, how many beetles will there be two years from now?

Please help I don't understand how to do this

Steve · Accepted Answer

P(n) = 20000(2^n)
Let now be when n=0
four years ago, n = -4, so
P(-4) = 20000(2^-4) = 20000/16 = 1250

Now do the same for n = -8 and n=2

You don't really need to set n=0. Suppose we started k years ago. That means that now would be P(k).

So, 4 years ago would be P(k-4) = P(k)/2^4 = 20000/16