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## Video transcript

- [Voiceover] Today, Nate has 100 bananas. He will eat two of them every day. Is the number of bananas Nate has left proportional to the number of days that pass? And I encourage you to pause this video and think about this. And what's interesting here, they're not saying, is the number of bananas eaten, they're saying the number of bananas Nate has left, proportional to the number of days that pass. So let's draw a little table here to think about this a little bit more. So I'm gonna make three columns. I'm gonna make three columns. So in the first column, this is gonna be the number of days that pass. So number of days... that pass. So that's this right over here, the number of days that pass. And this middle column, I'm gonna write the number of bananas Nate has left. Number of bananas... bananas left. And over here, I'm gonna make the ratio between the two. In order for this to be a proportional relationship, the ratio between these two has to be constant. So bananas left. So I'm gonna divide the second column by the first column. Bananas left... left, divided by days passed. Days passed. All right, so let's think about it a little bit. When one day has passed, how many bananas will he have left? Well, in that one day he will have eaten two bananas, so you're going to have 98 bananas left. And so what's the ratio of bananas left to days passed? Well, it's 98 over one, which is going to be equal to 98. All right. When two days have passed, how many bananas is he gonna have left? Well, he's going to consume two more bananas, so he's going to have 96 left, and so what's the ratio? It's going to be 96 to two, which is equal to 48. So clearly this ratio is not constant. It changed just from going to one day to the next day. So we don't have a constant ratio of bananas left to days passed, so this is not, this is not a proportional, proportional relationship. Now, things might've been a little bit different if they said the number of bananas Nate has eaten, is that proportional to the number of days that passed? Well, yeah, sure, because then, if this was the number of bananas eaten, if this was the number of bananas eaten, then it would always be two times the number of days that pass, so that would be two, and then that would be four, and then these ratios would always be two. But that's not what they asked for. They wanted us to compare number of bananas left to number of days that pass.