00:01
In this problem, you're working with an exponential growth model, and the reason i know that, or you would know that, is because it says that you're growing at a constant relative growth rate.
00:14
And the relative growth rate is defined by k equals dpdt times p, which then gives us our growth, the growth rate of dpdt, equals kp.
00:33
And that combination tells me that this is going to be an exponential growth.
00:40
First thing i know is that the initial population is given.
00:44
So i know that.
00:46
And i know the population after three days is 1720.
00:52
In order to write the model, i need to know what c and k are equal to.
00:58
So that's the first.
01:00
It says to write the model and round k to four decimal places.
01:05
So let's go ahead and do that.
01:07
So i know that first, at three days, i have a population of 7 ,220 is equal to the initial population, some of 250 e to the 3k.
01:34
All right, so the first thing we'll do is divide by 250.
01:41
So we'll do 1720 divided by 250.
01:50
And that'll give a value of 6 .88.
01:58
Next thing, we'll take the ln of both sides.
02:12
And taking the ln is what allows us to bring this variable exponent down front.
02:18
And also remember that ln of e.
02:22
Is equal to 1.
02:25
All right, so now we'll have ln of 6 .88.
02:31
Whoops, 6 .88.
02:35
Penn's not working right.
02:39
It's equal to 3k.
02:42
Then k will divide both sides by 3.
02:48
So, ln of 6 .88, divided by 3.
02:56
4 decimal places, 0 .6, 4, 29.
03:06
All right, so now we can write the model.
03:09
The model is going to be p, so this is letter a.
03:16
P is equal to the initial population of 250, e to the ln, nope, nope, not ln, to 0 .6429t.
03:38
All right, and we started out...