Population growth rate based on birth and death rates | Ecology | AP Biology | Khan Academy

When you take an AP Biology exam, it is likely that it will include a formula sheet that will include formulas like this on it. It can be a little bit intimidating at first because we're not used to seeing formulas like this that involve—in fact, this is formerly calculus notation—in a biology class. But what we'll see in this video is that this formula is actually just trying to express something that's fairly intuitive and something that you actually don't even need calculus or even much algebra. Then we'll connect it to this to see that it all makes sense.

So putting this aside, let me just ask you a simple question. Let's say we're studying a population, and we see that the birth rate of this population is equal to 60. Let's say we're studying a population of bunnies: 60 bunnies per year. And let's say we know that the death rate of bunnies is equal to 15 bunnies per year. Now, without even paying attention to this formula sheet up there, what do you think, given this data, is the population growth rate for this population of bunnies? Pause this video and see if you can answer that.

Well, your population growth rate—if you think about just even say a given year—in that year, you'll grow your population by 60 bunnies per year. So you will grow by 60 bunnies per year, and then you would shrink by the 15 that died. So it would shrink by 15 bunnies per year. In that year, you would net out 45 bunnies, and that's a rate, because you're saying per year. So you would grow by 45 bunnies in that year, and that would be your population growth rate.

Now, the thing that we just did very intuitively—you don't need advanced math to think through what we just did—that's exactly what this formula is saying. This notation, where you say d something dt, is the rate at which this something is changing with respect to time. So this is just a fancy way of saying, what is the rate at which our population is changing with respect to time?

There are other ways that you could have written that. If you didn't want to use calculus notation, you could have written change in population for a given change in time. The Greek letter delta often denotes change in. What this formula says is exactly what we did: it would be the difference between the birth rate, which is the letter b in this formula, and the death rate, the death rate is the letter d in this formula. You have it right over here, and that's exactly what we did over there. So it's all very intuitive.

Now, if I were in charge of the formula sheet, I might have expressed it a little bit different. Maybe I would have used notation like this; maybe I would have written in plain English. I probably would have used different notations for the b and the d to make it a little bit clearer that those were rates. But as you see from this example, it's just trying to express something very straightforward and frankly something that you probably actually don't need a formula sheet for.