MA131
0
: Module
2
Exponential a
nd Logarithmic Functions
Exercise 2
.2
Solving Exponential and Logarithmic
Equations
1
Answer the following questions to complete this exercise:
1.
Solve the following exponential equation by expressing each side as a power of the same base and
then equating exponents:
6
x
= 216
2.
Solve the following exponential equation:
e
x
= 22.8
Express the solution in terms of natural logarithms. Then, use a calculator to obtain a decimal
approximation for the solution.
3.
Solve the following logarithmic equation:
log
7
x
= 2
Reject any value
of
x
that is not in the domain of the original logarithmic expression. Give the exact
answer.
4.
Solve the following logarithmic equation:
log (
x
+ 16) = log
x
+ log 16
Reject any value of
x
that is ...view middle of the document...
When will the population of the state reach 23.3 million?
6.
The goal of our
financial security depends on understanding how money in savings accounts grows
in remarkable ways as a result of compound interest. Compound interest is computed on your
original investment as well as on any accumulated interest. Complete the table for a
savings account
subject to four compounding periods yearly.
Use the following
formula to solve this problem:
1
nt
r
AP
n
MA131
0
: Module
2
Exponential a
nd Logarithmic Functions
Exercise 2
.2
Solving Exponential and Logarithmic
Equations
2
Amount
Invested
Number of
Compounding
Periods
Annual
Interest Rate
Accumulated
Amount
Time
t
in
Years
$15,500
4
5.75%
$30,000
?
7.
Cell division is the growth process in many living organisms such as amoebas, plants, and human
skin cells. Based on an ideal situation in which no cells die and no by

products are created, the
number of cells present at a given time follows
the law of uninhibited growth, which is an
exponential model.
00
( ) or ; 0
ktkt
ftAeAAek
A
0
=
A
(0): Original Amount (Initial Value)
A colony of bacteria grows according to the law of uninhibited growth. If 100 grams of bacteria are
present initially, and 250 grams are present after two hours, how many will be present after 4
hours? Note: Do not round the value of
k
.
8.
Radioactive materia
ls like uranium follow the law of uninhibited decay, which is an Exponential
Model. This decay causes radiation. All radioactive substances have a specific half

life, which is the
time required for half the radioactive substance to decay. Uninhibited radio
active decay is given by
the formula:
0
( ) , 0
kt
AtAek
The half

life of thorium

229 is 7,340 years. How long will it take for a sample of this substance to
decay to 20 percent of its original amount?