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## Problem solving and data analysis

Current time:0:00Total duration:2:06

# Linear and exponential growth — Harder example

## Video transcript

- [Instructor] We're told
Sam needs to sign 300 copies of their new novel. They sign the copies at a constant rate. After 15 minutes, they have signed 20% of the copies. Which of the following equations models the number of copies
of Sam's new novel, N, left assign T minutes
after they started signing? So pause this video and see if you can have a go at this on your own. All right, now let's work
through this together. So when I look at the choices, we have an exponential for choice A, exponential for choice B, and then we have two linear functions for choices C and D. Well, they tell us that they signed, Sam signs the copies at a constant rate. So if we're signing at a constant rate, an exponential is not going to describe either how many we've signed
or how many are left to sign. So we can immediately
rule out choices A and B. So to figure out between
these last two choices, let's set up a little
table here where we know that T is in minutes and N is a number of books left to sign. And they tell us after 15 minutes they have signed 20% of the copies. So after 15 minutes,
what's end going to be? Well, N is the number
of books left to sign. So that means that there's
80% of the books left to sign, 80% of the original number of books. 80% times 300 is going to
be 240 books left to sign. So let's see which of these
choices is consistent with that. So 300 minus four times 15. Let's see, 300 minus four times 15. That does indeed look like 240. So this one's looking good. What about 300 minus 20 times 15? Well, 20 times 15 is 300. So that means that N would be zero here. We know that Sam doesn't have, isn't done signing after 15 minutes. So we could rule this choice
out and we like choice C.