00:01
We now write a function to represent the rabbit population t years after january 1, 2011, when the population of the rabbit is 24 on january 1, 2011.
00:12
And we are also told that the number of rabbits are tripled each year.
00:17
So i'm going to use this population model that is p of t and this equals p .0 n raised to the power of t by this upper case.
00:29
Low uppercase t let me explain the terms in this model this represents the population of the rabbits population of rabbits after t years and p .0 represents the initial population of the rabbits this is initial population and the n represents whether it is tripling or doubling.
01:02
Suppose if the population doubles we see that n equal to 2.
01:07
If the population triples, we say that n equal to 3.
01:11
So basically this n represents whether it doubles, triples, or each other.
01:17
And then this t is the general t, which represents the time in years or in terms of units of time.
01:24
And then this uppercase t, this represents how frequently the population doubles or triples.
01:31
So it doubles here in this question.
01:34
We see that it triples each each year so we say that t equals one here and so let's write down the model now i'm going to round down this as p of t and this equals we know that initial population is 24 that is on january 1 2011 we consider it as an initial population so we can write down 24 times and we know that the population doubles each other each each each year so i'm going to put n as 3 and then raise to the power of t divided by 80 triples each year.
02:14
So therefore we already mentioned that capital t equal to 1.
02:18
So i'm going to put this as 1.
02:21
So we can simplify and relate in proper expression.
02:26
That is we say that p of t and this equals 24 times 3 power t.
02:38
Is the function which represents the number of rabbits t years after january 1 2011.
02:47
Let's answer part b.
02:50
Here we have to determine the number of rabbits in january 1, 2020.
02:54
So we can use this model which we found in part a, that is p of t equals 24 times 3 raised to the power of t.
03:03
And so to use this model we have to determine t.
03:06
So t represents the number of years after january 1, 2011.
03:11
So if we look at the t, the starting year is 2011 and we have to determine the number of rabbits in 2020.
03:19
So it's basically we have to determine t and this equals 2020 minus 2011 and this equals 9...