00:01
All right, we are given a population of rabbits function n of t equivalent to 40 times b to the t, where t is bigger than or equal to 0.
00:11
We're going to answer part b and c here.
00:14
First thing we're going to do, we're going to answer a, b, and c, it looks like.
00:18
So first thing we're going to do is we're going to find the value of b.
00:22
We're given that initially we had 40 rabbits, and then one month later, the number of rabbits was doubled.
00:29
So i know that t, which is in months, when t occurred, we had 80 rabbits times b to the first, which is just 40b.
00:40
So if i solve for that, it looks like i end up getting b equals 2.
00:48
So b is equal to 2 here, because after one month, my population doubled.
00:53
Good.
00:54
So that's the first one.
00:56
The part b wants us to figure out the number of rabbits on the island, this was part a, after four months.
01:03
Well, now that we have our formula, given part a, n of t is 40 times 2 to the t.
01:08
I just plug in t equals 4, so i get 40 times 2 to the fourth, which is 40 times 16.
01:15
40 times 16 is 640.
01:25
There we go.
01:26
Now for part c, it says an ecologist estimates that the island has enough food to support a maximum population of 2560 rabbits...