1
MA 15200
Lesson 30
Exponential and Logarithmic Application Problems
In order to solve the applied problems in this lesson, a student must know how to use the
log, ln,
x
e
,
and power key functions on a scientific calculator.
There are lots of real life problems that have formulas with exponential or logarithmic
expressions.
The examples found in this lesson are just some.
Ex 1:
HalfLife of an Element
The
halflife
of an element is the amount of time necessary for the element to decay to
half the original amount.
Uranium is an example of an element that has a halflife.
The
halflife of radium is approximately 1600 years.
The formula used to find the amount of
radioactive material present at time
t
, where
A
0
is the initial amount present (at
t
= 0), and
h
= halflife of the element is
/
00
22
t
th
h
A
A
or A
A
.
Tritium, a radioactive isotope of hydrogen, has a halflife of 12.4 years.
If an
initial sample has 50 grams, how much will remain after 100 years?
Round to 4
decimal places.
Ex 2:
Population Growth
Another formula represents the population growth of lots of cities, towns, or countries.
The formula is
kt
e
P
P
0
where
P
is the final population,
P
0
is the initial population at
time 0,
t
is time in years, and
k
=
b

d
(
b
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 Fall '09
 Radioactive Decay, Decibel, Logarithm, Richter magnitude scale, Annual growth rate

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