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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 going to make three columns I'm going to make three columns so in the first column this is going to be the number of days that pass so days number of days that pass so that's this right over here the number of days that pass and this middle column I'm going to write the number of bananas Nate has left number of bananas bananas bananas left and over here I want to 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 going to divide the second column by the first column bananas left left divided by days passed days days passed all right so let's think about it a little bit when is when one day has passed how many bananas will he have left well 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 two days past was 98 over 1 which is going to be equal to 98 all right when two days have passed how many bananas is going to have left well he's going to consume two more bananas so he's going to have a 96 left and so what's the ratio it's going to be 96 to 2 which is equal to 40 which is equal to 48 so clearly this ratio is not constant it changed just from going from one day to the next day so we don't have a constant ratio of bananas left two days past so this is not this is not a proportional proportional proportional relationship now things might have 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 if this was a number of bananas eaten if this was the number of bananas eaten then it would always be two times the number of days at paths so that would be two and that would be four and then this then these ratios would always be two but that's not that's not what they asked for they they wanted us to compare a number of bananas left to number of days that pass