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Exponential Growth and Decay - Concept

Teacher/Instructor Carl Horowitz
Carl Horowitz

University of Michigan
Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

Exponential decay refers to an amount of substance decreasing exponentially. Exponential decay is a type of exponential function where instead of having a variable in the base of the function, it is in the exponent. Exponential decay and exponential growth are used in carbon dating and other real-life applications.

So exponential growth and decay refers
to an amount of substance either
growing or decreasing exponentially.

So what the formula your book is typically
going to be using is this N is equal
to N with this little 0 E to the RT.
What this N is you can either
hear it N 0 or N sub 0.
Either way basically it's
your initial amount.

In general I tend not to be so fond of this
equation because it's just another
equation for me to memorize.
What I want to do is draw some comparisons
how it's exactly the same thing as
our PERT equation which we'll use for
compounded continuously interest.

So basically what we have is N 0 or N sub
0 as our initial amount which corresponds
directly to P which is our principal
or initial amount. We have E to the RT.
Those are exactly the same.
Rate isn't exactly as it was like with a
percent like we want to have interest
that's 4. .04 goes in.
It's a little bit more abstract.
Little bit typically a complicated number but
still a rate that relates to this problem.

T is still time for our exponential growth.
It could vary, be in days, hours, whatever it is.
But it's still just a time.
This term by itself on the left is
going to be the ending amount.

So it's another equation but it's really
the exact same thing as PERT which
we already know.
The one other thing we need to talk about
is distinction between exponential
growth and decay.
That's really easy as well.

Exponential growth means something
is getting bigger.
You think of the whole scenario with rabbits
multiplying rapidly, that's exponential

And how that actually pans out is if this
R, this rate is going to be positive,
then our terms are growing.
We're getting bigger.
If this R is negative, then our terms
are going to be getting smaller.
That will be decay.

So exponential growth and decay.
It's a different formula.
But it's really exactly the same as our PERT
formula, just some different letters
thrown in the mix.

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