00:01
In this question, we are told that the population of a city is 900 ,000 people in 2018.
00:08
So, 2018 is our starting point and it corresponds to t equals 0.
00:13
So p of 0 equals to 900 ,000.
00:16
Now the population in 2020 is 800 ,000, and since 2020 is 2 years after 2018, 2020 corresponds to t equals 2.
00:27
So p of 2 equals to 800 ,000.
00:30
And we are asked to find the population in 20 and 22, and since 2022 corresponds to t equals 4, we need to calculate p of 4.
00:41
We are also told that the population in the city follows an exponential model.
00:48
So first, we need to find that model.
00:51
Since it's exponential, this means it must be of the form, p of t equals to some constant c multiplied by a multiplied by a to the power.
01:01
Of t.
01:03
We need to find c and a.
01:06
From the first condition, p of 0 equals to 900 ,000 people.
01:18
On the other hand, if we plug in t equals 0 in the previous formula, we are going to get c times a to the 0.
01:24
And since a to 0 equals to 1, we are going to get c equals to 900 ,000, so c equals to p0, the initial population.
01:34
Therefore, p of t equals to 900 ,000 multiplied by a to the t.
01:42
Now we need to find the constant a.
01:45
To find a, we are going to use the second condition.
01:48
P of 2 equals to 800 ,000.
01:57
On the other hand, if we plug in t equals 2 in the previous formula, we are going to get 900 ,000 multiplied by a squared...