This video, we're going to talk about the exponential population growth model. And so as long as the per capita population growth rate or *r* is both positive and constant, any population will grow exponentially over time. And so this exponential population growth really just refers to uninhibited population growth, where the population growth is increasing proportionally with the population size. And therefore, as population size or *n* increases, the population growth rate or ΔnΔt will also continuously increase in a manner that is directly proportional. And so this perfectly directly proportional relationship between the population growth and the population size is unique to this exponential population growth model.

Now exponential population growth does occur in nature, but it only occurs in very specific situations and over relatively short periods of time. And so exponential population growth is practically impossible in nature for long or extended periods of time because resources in nature are actually limited. And those limited resources somewhat inhibit or prevents populations from growing exponentially forever. And so notice that in a graph like the one down below where we have time on the x-axis and population size on the y-axis, exponential population growth will create somewhat of a curve that has a J shape, if you will, or because the *e* in exponential growth is somewhat unique, you could think of it as the shape of a lowercase *e* where the tail kind of curls up, if you will. So that could be helpful for some of you.

And again, any population will grow exponentially as long as the per capita population growth rate or *r* is both positive and constant, and that's always assumed to be the case in the exponential population growth model. And so notice that for this particular curve, the *r* is indicated as 1.0. Now also recall from previous lesson videos that there is a maximum per capita population growth rate or a maximum *r* value that is species-specific and only occurs under ideal conditions, and we refer to this as the *r _{max}* value. And so also recall that the greater the value of

*r*, the faster the population size will increase. And so if we assume that the

*r*value here is 1.5, then we can expect the exponential growth curve to increase even faster and look something like that.

_{max}And again, if the *r* value is smaller like 0.5, then it can still grow exponentially, it'll just grow slower. So the exponential curve might look something like this, for example. And so this here concludes our lesson on the exponential population growth model. Moving forward, we'll be able to apply these concepts, and then we'll talk about the equations for this exponential population growth model. So I'll see you all in our next video.