**Unformatted text preview: **Applications of Exponential
Functions
Functions
Section 5.3 Compound Interest
Compound If
If P dollars is invested at interest rate r
(expressed as a decimal) per time period t,
then A is the amount after t periods. A = P (1 + r ) t Continuous Compounding
Continuous If
If P dollars is invested at an annual interest
rate of r, compounded continuously, then A is
compounded
the amount after t years.
years. A = Pe rt Exponential Growth
Exponential
Exponential growth can be described by a function
Exponential
of the form
x f ( x) = Pa Where f(x) is the quantity at time x, P is the initial
f(x)
quantity when x = 0 and a >1 is the factor by
which the quantity changes when x increases by
1. If the quantity f(x) is growing at rate r per time
If
f(x)
period, then a = 1 + r and f ( x) = Pa = P (1 + r )
x x Exponential Decay
Exponential
Exponential decay can be described by a function of
Exponential
the form
x f ( x) = Pa Where f(x) is the quantity at time x, P is the initial
f(x)
quantity when x = 0 and 0 < a < 1 is the factor by
which the quantity changes when x increases by
1. If the quantity f(x) is decaying at rate r per time
1.
f(x)
period, then a = 1 - r and f ( x) = Pa = P (1 − r )
x x Radioactive Decay
Radioactive
The amount of a radioactive substance that
remains is given by the function
remains f ( x) = P (0.5) x
h Where P is the initial amount of the substance, x =
0 corresponds to the time when the radioactive
decay began and h is the half-life of the
half-life
substance.
substance. Joke Time
Joke
What
What has wings and solves
number problems?
number A mothematician What
What did one math book say
to the other math book?
to Don’t
Don’t bother me! I’ve got my
own problems!
own ...

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