00:01
Okay, so we are given that the birth rate follows this equation.
00:10
B of t equal to 4 .8 minus 0 .04 t squared, and that the death rate follows 4 plus 0 .01 t squared.
00:35
And we're also given that.
00:37
The start of 1990 there was 2 ,000 people or 200 ,000 people.
01:02
Yeah, we can write that.
01:05
This is a population.
01:11
Okay, so we first want to know, we want to know the total number of births between 1990 and the end of 1999.
01:30
So in that case, we have tdb9.
01:36
And we plug that into our equation, 4 .8.
01:41
Minus 0 .0 .04 times 9 squared.
01:59
So 4 .8 minus 0 .04 times 81.
02:10
That would be 1 .56.
02:14
So these are measured in thousands.
02:22
So 1 .56 ,000.
02:28
Actually, we need to do, we have to set this up with an integration instead.
02:37
So from 0 to 9 of 4 .8 minus 0 .04t squared dt.
02:50
Just be 4 .8 minus 0 .04t cubed.
03:02
It should be a t right here, cube.
03:10
And then from 9 to 0 to 9.
03:15
So when we plug in an upper bound of 9, so 4 .8 times 9 minus 0 .04 times 9 cubed divided by 3.
03:34
That's going to be 33 .48.
03:42
Then when we plug in 0, a lower balance is going to be 0.
03:46
So therefore there is 33 .48 ,000 births in that time frame.
04:05
Now we want to know how many deaths were in that same period.
04:12
So we're going to do 0 to 9 of 4 plus 0 .01 t squared d t.
04:25
T says it's going to be 4t plus 0 .01 t cubed over 3 from 0 to 9 so plug in 9 here so we have 4 times 9 plus point 0 .01 times 9 cubed over 3 so we'll get 38 .43 so then minus 0 for the lower about so we had 38 .43 ,000 deaths in that time frame.
05:32
So we want to know what is the population of the city at the start of the year 2000.
05:43
So in this case, this is 10 years later.
05:47
So we're going to take the initial population of 200 ,000, and we're going to add that to the death rate and the birth rate over that time frame.
05:55
So let's figure out, let's, we need to do all that in the integration...