00:01
In this question we are told that there were initially 120 rabbits and their population doubles every 6 months.
00:09
And we are asked to find the growth rate constant a in this formula.
00:21
And to do that, first of all we know that p0 equals 120, the initial population.
00:27
Also, we know that the population doubles every 6 months.
00:32
So that means after 6 months we expect the population to be 240.
00:39
Here t is in month.
00:46
So if we plug in t equals 6 we are supposed to get 240 rabbits.
00:50
On the other hand, p of 6 by this formula here equals 120 multiplied by a to the 6.
01:01
And they must be equal.
01:04
So we'll get the equation 120 a to the 6 equals 240.
01:11
And after dividing by 120 we'll get a to the 6 equals 2.
01:17
And after taking the 6 root we'll get a equals 2 to the 1 over 6.
01:25
So this is a growth rate constant.
01:28
And the formula for the population will be p of t equals 120 multiplied by 2 to the 1 over 6 to the power of t.
01:39
And this could be written as 120 multiplied by 2 to the t over 6...