00:01
Here we're given a situation where the population grows at a rate proportional to the number of people at any given time.
00:06
So that means that y is going to be according to pert, p e to the r t.
00:14
And then we told that it doubles in five years.
00:16
So we're going to get 2p in five years.
00:19
So i could say 2 is equal to r times 2.
00:23
Well that means that 2r is equal to ln of 2, or r is equal to ln of 2 so we now know r.
00:32
Next we're told the population is 10 ,000 after three years.
00:36
Well so let's just say 10 ,000 is equal to p, which we don't know, e to the r, which we do know, times 3.
00:47
So if i'm solving for p, p is going to be 10 ,000 divided by e to the 3r, which we know all of these things.
00:56
So now we would just want to know what was the initial population.
00:59
Well that's p...