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MAT-1210: COLLEGE ALGEBRA
Kristi Stevenson
Practice Exercises 9
SECTION 6.1
Algebraic
For the following exercise, identify whether the statement represents an exponential function. Explain.
1.
The height of a projectile at time is represented by the function
h
(
t
)=−
4.9
t
2
+
18
t
+
40
.
This is not an exponential function it is a polynomial function. It does not follow the exponential
formula of f(x) = ab
x
For the following exercise, consider this scenario: For each year the population of a forest of trees is
represented by the function
A
(
t
)=
115
(
1.025
)
t
.
In a neighboring forest, the population of the same
type of tree is represented by the function
B
(
t
)=
82
(
1.029
)
t
.
(Round answers to the nearest whole
number.)
2.
Which forest had a greater number of trees initially? By how many?
A
(
t
)=
115
(
1.025
)
t
A(t)
has a greater number of trees by 34.
For the following exercise, determine whether the equation represents exponential growth, exponential
decay, or neither. Explain.
3.
y
=
16.5
(
1.025
)
1
x
The equation is neither growth nor decay since the exponent in the form of
1
x
is not an
exponential equation.
For the following exercise, find the formula for an exponential function that passes through the two points
given.
4.
(
3,1
)
∧
(
5,4
)
This work, “Practice Exercises 9,” is a derivative of
College Algebra 2e
by Jay Abramson, OpenStax used under
CC BY 4.0
.
“Practice Exercises 9” is licensed under CC BY 4.0 by Thomas Edison State University.
For the following exercise, use the compound interest formula,
A
(
t
)=
P
(
1
+
r
n
)
nt
.
5.
After a certain number of years, the value of an investment account is represented by the
equation
A
(
t
)=
10,250
(
1
+
r
0.4
12
)
120
What is the value of the account?
After 10 years the value of the account is $524,296.02
Numeric
For the following exercise, evaluate each function. Round answers to four decimal places, if necessary.
6.
f
(
x
)=
2.7
(
4
)
−
x
+
1
+
1.5
, for
f
(−
2
)
Technology
For the following exercise, use a graphing calculator to find the equation of an exponential function given
the points on the curve.
7.
(
3,222.62
)
∧
(
10,77.456
)
.
f
(
x
)=
350.000032
(
0.8600004889
)
x
Real-World Applications
8.
A scientist begins with 100 milligrams of a radioactive substance that decays exponentially. After
35 hours, 50 mg of the substance remains. How many milligrams will remain after 54 hours?
This work, “Practice Exercises 9,” is a derivative of
College Algebra 2e
by Jay Abramson, OpenStax used under
CC BY 4.0
.
“Practice Exercises 9” is licensed under CC BY 4.0 by Thomas Edison State University.
This work, “Practice Exercises 9,” is a derivative of
College Algebra 2e
by Jay Abramson, OpenStax used under
CC BY 4.0
.
“Practice Exercises 9” is licensed under CC BY 4.0 by Thomas Edison State University.
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9.
Kyoko has $10,000 that she wants to invest. Her bank has several investment accounts to
choose from, all compounding daily. Her goal is to have $15,000 by the time she finishes
graduate school in 6 years. To the nearest hundredth of a percent, what should her minimum
annual interest rate be in order to reach her goal? (Hint: Solve the compound interest formula for
the interest rate. Note: banks use 360 for
n
when compounded daily.)
SECTION 6.2
For the following exercise, graph each set of functions on the same axes.
10.
f
(
x
)
=
1
4
(
3
)
x
, g
(
x
)=
2
(
3
)
x
,
∧
h
(
x
)=
4
(
3
)
x
.
This work, “Practice Exercises 9,” is a derivative of
College Algebra 2e
by Jay Abramson, OpenStax used under
CC BY 4.0
.
“Practice Exercises 9” is licensed under CC BY 4.0 by Thomas Edison State University.
For the following exercise, graph the function and its reflection about the x-axis on the same axes.
11.
f
(
x
)=
3
(
0.75
)
x
−
1
For the following exercise, graph the transformation of
f
(
x
)=
2
x
.
Give the horizontal asymptote, the
domain, and the range and describe the end behavior.
12. .
f
(
x
)=
2
x
−
2
H.A. – 0.25
D: (-∞, ∞)
R: (0, ∞)
E.B.:
f
(
x
)
→∞
This work, “Practice Exercises 9,” is a derivative of
College Algebra 2e
by Jay Abramson, OpenStax used under
CC BY 4.0
.
“Practice Exercises 9” is licensed under CC BY 4.0 by Thomas Edison State University.
For the following exercise, start with the graph of
f
(
x
)=
4
x
.
Then write a function that results from
the given transformation.
13. Reflect
f
(
x
)
about the
x
axis.
f
(
x
)
=−
4
x
Numeric
For the following exercise, evaluate the exponential function for the indicated value of
x
.
14.
f
(
x
)=
4
(
2
)
x
−
1
−
2,
for f
(
5
)
❑
.
This work, “Practice Exercises 9,” is a derivative of
College Algebra 2e
by Jay Abramson, OpenStax used under
CC BY 4.0
.
“Practice Exercises 9” is licensed under CC BY 4.0 by Thomas Edison State University.
Your preview ends here
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Technology
For the following exercise, use a graphing calculator to approximate the solution of the equation. Round
to the nearest thousandth.
15.
12
=
2
(
3
)
x
+
1
.
X=1.551
SECTION 6.3
Algebraic
For the following exercise, rewrite the log equation in exponential form and the exponential equation in
logarithmic form.
16. a)
log
y
(
x
)=−
11
b)
x
−
10
13
=
y
Numeric
For the following exercise, evaluate the base logarithmic expression without using a calculator.
17.
log
2
(
1
8
)
+
4
This work, “Practice Exercises 9,” is a derivative of
College Algebra 2e
by Jay Abramson, OpenStax used under
CC BY 4.0
.
“Practice Exercises 9” is licensed under CC BY 4.0 by Thomas Edison State University.
For the following exercise, evaluate the natural logarithmic expression without using a calculator.
18.
ln
(
e
−
0.225
)
−
3
Real-World Applications
19.
The exposure index
EI
for a camera is a measurement of the amount of light that hits the
image receptor. It is determined by the equation
EI
=
log
2
(
f
2
t
)
where
f
is the “f-stop” setting
on the camera, and
t
is the exposure time in seconds. Suppose the f-stop setting is
8
and the
desired exposure time is
2
seconds. What will the resulting exposure index be?
This work, “Practice Exercises 9,” is a derivative of
College Algebra 2e
by Jay Abramson, OpenStax used under
CC BY 4.0
.
“Practice Exercises 9” is licensed under CC BY 4.0 by Thomas Edison State University.
SECTION 6.4
Algebraic
For the following exercise, state the domain, vertical asymptote, and end behavior of the function.
20.
f
(
x
)
=
log
3
(
15
−
5
x
)
+
6
E.B.:
As x →
−
∞ ,f
(
x
)
→
−
∞ , As x→∞ ,f
(
x
)
isundefined
This work, “Practice Exercises 9,” is a derivative of
College Algebra 2e
by Jay Abramson, OpenStax used under
CC BY 4.0
.
“Practice Exercises 9” is licensed under CC BY 4.0 by Thomas Edison State University.
Your preview ends here
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Graphical
For the following exercise, sketch the graphs of the pair of functions on the same axis.
21.
f
(
x
)=
log
4
(
x
)
∧
g
(
x
)=
ln
(
x
)
For the following exercise, sketch the graph of the indicated function.
22.
h
(
x
)=
−
1
2
ln
(
x
+
1
)
−
3
This work, “Practice Exercises 9,” is a derivative of
College Algebra 2e
by Jay Abramson, OpenStax used under
CC BY 4.0
.
“Practice Exercises 9” is licensed under CC BY 4.0 by Thomas Edison State University.
For the following exercise, write a logarithmic equation corresponding to the graph shown.
23. Use
f
(
x
)=
log
5
(
x
)
as the parent function.
f
(
x
)
=−
2log
5
(
−
x
)
+
5
Technology
For the following exercise, use a graphing calculator to find an approximate solution to the equation.
24.
2ln
(
5
x
+
1
)
=
1
2
ln
(
−
5
x
)
+
1
x= -0.018399
x= -0.1930107
This work, “Practice Exercises 9,” is a derivative of
College Algebra 2e
by Jay Abramson, OpenStax used under
CC BY 4.0
.
“Practice Exercises 9” is licensed under CC BY 4.0 by Thomas Edison State University.