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# Exponential vs. linear growth

CCSS.Math:

## Video transcript

so I have two different XY relationships being described here and what I would like to do in this video is figure out whether each of these relationships whether they are either linear relationships exponential relationships or neither and like always pause this video and see if you can figure it out yourself so let's look at this first relationship right over here and the key way to tell whether we're dealing with a linear or exponential or neither relationship is think about okay for given change in X and U here you see each time here we are increasing X by the same amount so we're increasing X by 3 so given that we are increasing X by a constant amount by 3 each time those Y increase by a constant amount in which case we would be dealing with a linear relationship or is there a constant ratio between successive terms when you increase X by a constant amount in which case we would be dealing with an exponential relationship let's see here we're going from negative 2 to 5 so we are adding 7 when x increases by 3 y increases by 7 when X is increasing by 3 y increases by 7 again what x increases by 3 y increases by 7 again so here it is clearly a linear relationship linear relationship in fact you can even relationship you could even plot this on a line if you assume that these are samples on a line you could think even about the slope of that line for a change in X for a given change in X the change in Y is always constant when our change in X is 3 our change in Y is always 7 so this is clearly a linear relationship now let's look at this one let's see looks like our X's are changing by one each time so plus one now what our Y is changing by here it changes by two then it changes by six is clearly not linear then it changes by 18 clearly not a linear relationship this was linear this would be the same amount same Delta same change in Y for every time because we have the same change in F so let's test to see if it's exponential if it's an exponential for each of these constant changes in X's when we increase X by 1 every time our ratio of successive Y should be the same or another way to think about is what are we multiplying Y by so to go from 1 to 3 you multiply you multiply by 3 to go from 3 to 9 you multiply by 3 to go from nine to 27 you multiply by 3 so in a situation where every time you increase X by a fixed amount in this case 1 and the corresponding Y's get multiplied by some fixed amount then you are dealing with an exponential relationship exponential exponential relationship right over here