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## AP®︎/College Biology

### Course: AP®︎/College Biology > Unit 8

Lesson 3: Population ecology- Exponential and logistic growth in populations
- Exponential & logistic growth
- Population regulation
- Population regulation
- Population growth rate based on birth and death rates
- Per capita population growth and exponential growth
- Logistic growth versus exponential growth
- Population ecology review
- Population ecology

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# Population growth rate based on birth and death rates

Calculating population growth rate is simpler than it seems. By comparing birth and death rates, we can intuitively find the growth rate. Here, we show the formula to calculate population growth rate, using calculus notation. Although this formula may look intimidating, it represents a straightforward concept, making it easy to grasp and apply in biology.

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- I'm assuming you take immigration and emigration into account as well, correct?(4 votes)

## Video transcript

- [Instructor] When you
take an AP Biology exam it is likely that will
include a formula sheet that will include formulas like this one and 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
formally 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, but 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, the birth rate of this population is equal to 60, let's say we're studying
a population of bunnies, 60 bunnies, bunnies per year and let's say we know that
the death rate of bunnies, death rate, is equal to 15 bunnies, bunnies per year. Now, without even paying attention to this formula sheet up there, what do you think, given this data, is the population, 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, bunnies per year and so in that year you
would net out 45 bunnies and that's a rate 'cause
you're saying per year. So you would grow by 45 bunnies, 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's saying. This notation where
you say d something dt, this 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's other ways that you
could have written that. If you didn't wanna use calculus notation you could of written change in population for a given change in time. The Greek letter delta
often denotes change in and 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, the birth rate, right over here, 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.