00:02
All right, so for this one here, a company finds that it sales since the company started in 2000 can be modeled by the function.
00:10
S of t equals 20 t squared plus 800 t plus 300, all divided by 8t squared plus 10t plus 100, where s is the total sales in millions of dollars and t is the number of years since 2000.
00:27
Calculate the years when the sales are 9 million algebraically.
00:33
All right, so to do that algebraically, you would take this equation here and set it equal to nine first.
00:43
Then you would multiply nine times the denominator, and nine times eight is 72, nine times ten is 90, and nine times 100 is 900.
00:56
So that gets us this equation here, 20x squared plus 800x plus 300 equals, 72x squared plus 900x plus 900.
01:11
Then we move everything over to the right -hand side by subtracting 20x squared, 8 ,000x, and subtracting 300, and you get 52x squared minus 710x plus 600.
01:27
And then using the pythagorean theorem, 710 plus and minus the square root of 710 squared, minus 4 times 52 times 600, all divided by 104.
01:40
That will get you 12 .74 years when you do the plus answer, and it will get you 0 .905 years when you use to the minus answer.
01:56
So approximately at 2001 and 2012, close to 2013.
02:05
The other way to find those solutions is to type that equation in, which gives you this thing that looks like this.
02:14
And then put in an equation of y equals 9.
02:18
And here's the intersection point at 0 .905, which is the same as this minus answer down here.
02:25
And the 12 .749, which is the same as the plus answer.
02:34
Then the second part of the question says, what, as the years go by, what does the model predict sales will be? well, if we zoom out, you'll see that this kind of levels off over here to the right.
02:51
And if we zoom way out and do that in desmos, click on the gear button...