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Current time:0:00Total duration:3:14

AP.BIO:

SYI‑1 (EU)

, SYI‑1.G (LO)

when you take an AP biology exam it is likely that will include a formula sheet that will include formulas like this on it 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 formerly calculus notation in a biology class but 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 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 could 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 but 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 because 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 is 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 want to use calculus notation you could have brought written change in population for a given change in time the Greek letter Delta often denotes change in and what this form of says is exactly what we did it would be the difference between the birthrate which is the letter B in this formula the birthrate 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

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