- [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.
