00:01
Hi there, so for this problem, we will solve this problem using the exponential growth model, that the population at any given time, it is equal to the initial population times the aspenumptial of a constant key times the time.
00:18
Now, the condition that we are given for this is that after five, after five years, the population has doubled.
00:28
So that will be twice the initial population, okay? so we are going to substitute that condition in here.
00:35
So we evaluate that at five.
00:36
So that will be two times the initial population equals to the initial population times the exponential of five times the time.
00:44
And, sorry, five times key.
00:47
We can cancel the initial population with the initial population.
00:51
And then we have this.
00:55
Now, once we have this, what we are going to do is to solve for, we can just solve for the aspenamishal of key.
01:04
So the esponemical of key will be elevated in both sides to one divided by five.
01:15
Now once we have this, then we can write that the population at any given time.
01:21
It is equal to the initial population.
01:25
Then this times two elevated to one divided by five.
01:30
And sorry, in the timing here.
01:37
Okay, now the question, the first question is about the initial population p -sub -0.
01:47
So we know that we are given that the population after three years, it is 9 ,000...