Linear equations word problem: file transfer
About this video
Agent Hunt's drive holds S(t) = 5t + 45 megabytes after t seconds. Sal finds S(0) = 45 MB at the start and shows that every 10 seconds adds 50 MB, because the function rises by 5 for each second.
You'll be able to
- find the starting value of a linear function by evaluating it at t = 0.
- find how much a linear function changes over an interval.
- explain the rate of change in context.
Key words
- function of time
- A rule that gives an output, like file size, for each moment t.
- megabyte (MB)
- A unit for measuring the size of computer files.
- rate of change
- How much the output changes for each 1-unit increase in the input; here 5 MB per second.
Transcript
- [Voiceover] Agent Hunt is transferring classified files from the CIA mainframe into his flash drive. This is the formula for the size of the files on Agent Hunt's drive S, measured in megabytes, as a function of time t, measured in seconds. Complete the following sentences with the appropriate missing values.
When the transfer began, the drive had blank megabytes of files on it. So, when the transfer began, that would be t equals zero. T equals zero was right when the transfer began. So t equals zero. S of zero is going to be five times zero, five times zero plus 45, which of course is just going to be equal to 45.
And S is measured, and they tell us, measured in megabytes. So there were 45 megabytes of files on his drive before, or right when the transfer began. Then they say, every 10 seconds, every 10 seconds, an additional blank megabytes are transferred into the drive.
So every 10 seconds, how many? Well, one way to think about, there's a bunch of ways you could think about this one is, we know that there were 45 megabytes at time equals zero. Let's think about what happens 10 seconds later. How many megabytes are in his drive?
So we can say S of 10 is going to be five times 10 plus 45, which is equal to 50 plus 45. So, time equals zero there were 45 megabytes and 10 seconds later there's now 50 plus 45 megabytes. So in 10 seconds an extra 50 megabytes are transferred into the drive.
And that's expected, because as t increases one, this function goes up by five, so if t increases by 10, this is going to increase by 50. So for every 10 seconds you would have, 50 megabytes are transferred into the drive. And you can test that more if you want.
You can say okay, let's go another 10 seconds. S of 20 seconds, that's going to be 5 times 20 plus 45, which is equal to 100 plus 45. So notice, when 10 seconds have passed in time, when we've increased time by 10 seconds, we've increased memory, our memory that we're using, the megabytes we're using has increased by, has increased by, has increased by 50.
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