00:01
Here we have a question about growth rates.
00:03
So to begin with, we've released a population of 20 elephants into a park.
00:08
The growth is exponential with a her capita growth rate of 0 .08 per year.
00:13
What is the doubling time? okay.
00:17
So if x is the current population, we can express this as 20 times 1 .08 to the power of n, where n is how many years have passed.
00:32
So 1 .08 would just be 1 plus the growth rate, 0 .08.
00:38
And so you can see it is growing by 0 .08 per elephant per year.
00:44
So this is a very important equation.
00:47
You can generalise that you've got the initial condition, it being 20, the amount it grows by, which is 1 .08, and n being the number of years.
00:58
So we want the doubling time.
01:00
So how long does it take to go from 20 to 40? so we want x to be 40.
01:05
First thing we're going to do, divide both sides by 20.
01:08
So it's going to be 2 equals 1 .08 to the power of n.
01:17
Right.
01:18
Now we have to do some logarithmic stuff, because if we want n here, then we have to have log 1 .08 of 2 equals n...