00:01
That the function t of x is going to represent the total worldwide box office receipts for long -running movies, where t of x represents the amount of money, and x is the number of years since the movie's released.
00:13
So what we want to do first is find how fast are the total receipts changing from year one year, or from one year, five years and eight years after the release.
00:22
So i'm going to call part a the amount that would happen after one year.
00:27
Well, that would mean that x is equal to one.
00:30
All we're going to do is substitute 1 into our function.
00:33
So in other words, we're essentially finding t of 1.
00:36
So this would equal to 120 times 1 squared, all getting divided by 1 squared plus 4.
00:42
And now we just need to simplify.
00:44
Well, in the numerator, we have 1 squared which is 1, and 1 times 120 is just 120, divided by 1 squared is 1, 1 plus 4 is equal to 5.
00:53
So we're left with 120 divided by 5, which is equal to 24 million.
00:57
So, or 24.
00:58
But remember, this is in terms of millions of dollars.
01:01
So that would mean it would be $24 million would be expected to be the box offer receipts after one year.
01:08
Now, for part b, or i'm going to call this part b, what we want to do is find the total receipts after five years.
01:17
So let's go ahead and put that down.
01:19
So part b, we want five years.
01:21
So again, that just means that x, our x value, would end up equaling to five...