ACC: Study Guide Exponential Functions
____
1. Find the common difference in the arithmetic sequence
, ...
a. common
b. common
c. common
d. common
difference: 11
difference: –11
difference: –22
difference: 22
____
2. Find the next three terms in the arithmetic sequence
a.
b.
c.
____
d.
3. Determine a relationship between the x- and y-values. Write an equation.
1
2
3
4
x
4
5
6
7
y
a. y = x + 4
____
, ...
b. y = 3x + 1
d. y = –x + 3
c. y = x + 3
4. Determine whether the sequence appears to be an arithmetic sequence. If so, find the common difference and the next
three terms in the sequence.
–5, –11, –17, –23, –29, . . .
a. Yes; common difference 6; next three terms are –23, –17, –11
b. Not an arithmetic sequence
c. Yes; common difference –7; next three terms are –36, –43, –50
d. Yes; common difference –6; next 3 terms are –35, –41, –47
____
____
5. Find the 20th term in the arithmetic sequence –4, 1, 6, 11, 16,...
a. 95
b. 72
c. 96
6. Find the next three terms in the geometric sequence
a. –1, 6, –36
c.
b.
,
d.
,
d. 91
, 6,
,
,
,
,
, ...
,
____
7. The first term of a geometric sequence is 512, and the common ratio is 0.5. What is the 8th term of the sequence?
a. 22.63
b. 2
c. 4
d. 8
____
8. A computer is worth $4000 when it is new. After each year it is worth half what it was the previous year. What will
its worth be after 4 years? Round your answer to the nearest dollar.
a. $1000
b. $250
c. $125
d. $500
____
9. The function
, where x is the time in years, models a declining lemming population. How many
lemmings will there be in 6 years?
a. About 29,160
b. About 5,001
c. About 30,006
d. About 4,217
lemmings
lemmings
lemmings
lemmings
____ 10. Graph
.
y
a.
–5
–4
–3
–2
y
b.
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1
–1
–1
1
2
3
4
5 x
–5
–4
–3
–2
–1
–1
1
2
3
4
5 x
____ 11. Graph y = –(4)x.
a.
y
y
b.
5
15
–4
10
–3
–2
–1
1
2
3
4
x
5
x
–5
5
–10
–4
–3
–2
–1
1
2
3
4
x
–15
–5
____ 12. Graph
a.
.
y
–5
–4
–3
–2
y
b.
5
5
4
4
3
3
2
2
1
1
–1
–1
1
2
3
4
5
x
–5
–4
–3
–2
–1
–1
–2
–2
–3
–3
–4
–4
–5
–5
1
2
3
4
____ 13. The value of a gold coin picturing the head of the Roman Emperor Vespasian is increasing at the rate of 5 per year.
If the coin is worth $105 now, what will it be worth in 11 years?
a. $169.79
b. $160.00
c. $179.59
d. $162.75
____ 14. Write a compound interest function to model the following situation. Then, find the balance after the given number
of years.
$17,400 invested at a rate of 2.5% compounded annually; 8 years
a.
c.
; $391,826,318
; $26,550,293
b.
d.
; $21,200
; $84,504
____ 15. Graph the data set {(–1, 0.5), (0, 1), (1, 2), (3, 8), (5, 32)}. Which kind of model best describes the data?
a. linear
b. exponential
c. quadratic
d. cubic
____ 16. Look for a pattern in the data set. Which kind of model best describes the data?
Population Growth of Bacteria
Time (hours)
Number of
Bacteria
0
2,000
1
5,000
2
12,500
3
31,250
4
78,125
a. exponential
b. cubic
c. quadratic
d. linear
17. Rewrite the expression using positive exponents.
____ 18. Write 2,239 in scientific notation.
a. 2.239  103
b. 2.239  104
c.
d. 2.2390  101
____ 19. Write 0.000732 in scientific notation.
a.
b.
c.
d.
c.
d.
Multiply:
____ 20.
a.
b.
____ 21. In astronomy, the immense distances between celestial bodies are measured in light-years, the distance that light can
travel in one year. One light-year is approximately 5,880,000,000,000 miles. If a star is 8.4 light-years from Earth,
how would you correctly represents the number of miles the star is from Earth in scientific notation ?
a.
b.
c.
d.
____ 22. The calorie and the BTU (British Thermal Unit) are two standard units of energy. Two calories is about 0.007936
BTU. How is this measure expressed in scientific notation?
a.
b.
c.
d.
____ 23. Which list shows the numbers in order from least to greatest?
a.
b.
c.
d.
24. Write 732,000 in scientific notation.
25. Rewrite 0.00000428 in scientific notation.
26. Rewrite
27. Rewrite
28. Evaluate
in standard form.
in standard form.
. Write the result in standard form.
____ 29. The amount of money, A, accrued at the end of n years when a certain amount, P, is invested at a compound annual
rate, r, is given by
If a person invests $150 in an account that pays 10% interest compounded annually,
find the balance after 5 years.
a. $4800
b. $1650
c. $8250
d. $242
____ 30. Sara bought 7 fish. Every month the number of fish she has doubles. After m months she will have F fish, where
. How many fish will Sara have after 2 months if she keeps all of them and the fish stay healthy?
a. 196
b. 28
c. 20
d. 11
Graph the function.
31.
32. Find the value of $1000 deposited for 10 years in an account paying 7% annual interest compounded yearly.
33. How much money must be deposited now in an account paying 7% annual interest, compounded yearly, to have a
balance of $1000 after 6 years?
34. Write a rule for the function.
x
y
22
27
21
9
0
3
1
1
2
Write a rule for the function.
35.
36. Graph the function and label as exponential growth or decay.
37. Graph the function and label as exponential growth or decay.
(2)
y
5
–5
5
x
–5
38. Choose the equation that represents exponential decay.
a.
b.
Graph the function and label as exponential growth or exponential decay.
39.
(0.1)
y
5
–5
5
x
–5
40. The amount, A, of 96 grams of a certain radioactive material remaining after t years can be found by the equation
. How much radioactive material is left after 9 years? Round your answer to two decimal places.
41. The enrollment at Alpha-Beta School District has been declining 3% each year from 1994 to 2000. If the enrollment
in 1994 was 2583, find the 2000 enrollment.
Tell whether the graph represents exponential growth or exponential decay . Then write a rule for the
function.
42.
43.
Compare the graph of the function with the graph of
. Be specific (stretch/srhink by what factor,
reflection).
44.
45.
46.
Simplify. Leave your answer in exponential form.

____ 47.
a.
b.
c.
d.
____ 48.
a.
b.
c.
d.
____ 49.
a.
b.
c.
d.
a.
b.
c.
d.
a.
b.
c.
d.
a.
b.
c.
d.
____ 50.
____ 51.
____ 52.
Simplify the expression using positive exponents.
____ 53. Simplify
.
a.
b.
c.
54.
55. Evaluate the expression
.
d.
Simplify:
____ 56.
a.
b.
c.
d.
a. 252
b. 36
c. 14
d. 20
____ 57.
58. What is the value of the expression
59. Evaluate
.
60. The 7th term of a geometric sequence is 31.45728. The common ratio is –0.8. Find the first term of the sequence.
61. Solve the equation.
62. Rewrite using only positive exponents:
63. Rewrite the expression using positive exponents.
64. Rewrite the expression using positive exponents.
____ 65. Find the 16th term in the following arithmetic sequence.
–6, –13, –20, –27, –34, ...
a. –105
b. –118
c. –126
d. –111
____ 66. Determine if the sequence could be geometric. If so, give the common ratio.
3, –15, 75, –375, 1,875, ...
a. Not a geometric
b. yes; 5
c. yes; –4
d. yes; –5
sequence.
____ 67. What is the 16th term in the following geometric sequence?
5, –10, 20, –40, 80, ...
a. 163,840
b. 327,680
c. –163,840
____ 68. Create a table for the exponential function
, and use it to graph the function.
y
a.
–5
–4
–3
–2
d. –32,768
y
b.
5
5
4
4
3
3
2
2
1
1
–1
–1
1
2
3
4
5
x
–5
–4
–3
–2
–1
–1
–2
–2
–3
–3
–4
–4
–5
–5
69. a. Can a sequence be both arithmetic and geometric?
b. If so, name one.
1
2
3
4
5
x
ACC: Study Guide Exponential Functions
Answer Section
1. ANS: B
?
The terms decrease by 11. The common difference is –11.
Feedback
A
B
C
D
Find the increase or decrease from one term to the next term.
Correct!
Find the increase or decrease from one term to the next term.
The common difference is added to each term to get the next term.
PTS: 1
DIF: Average
REF: Page 142
OBJ: 3-6.1 Finding the Common Difference in an Arithmetic Sequence
NAT: 8.5.1.b
STA: M8A3.f
TOP: 3-6 Arithmetic Sequences
2. ANS: A
Each term is 7 less from the previous term.
?
Use the common difference to find the next three terms.
The next three terms are
.
Feedback
A
B
C
D
Correct!
Find a pattern from one term to the next term, and make sure that the pattern works for
all the terms.
Use the common difference to find the next three terms.
Use the common difference to find the next three terms.
PTS: 1
DIF: Average
REF: Page 142
OBJ: 3-6.2 Finding Missing Terms in an Arithmetic Sequence
STA: M8A3.f
TOP: 3-6 Arithmetic Sequences
3. ANS: C
The correct equation is y = x + 3.
1
2
3
4
x
4
5
6
7
x+3
NAT: 8.5.1.a
Feedback
A
B
C
Substitute the x-values into your equation to make sure they give the correct y-values.
Substitute the x-values into your equation to make sure they give the correct y-values.
Correct!
D
Substitute the x-values into your equation to make sure they give the correct y-values.
PTS: 1
DIF: Basic
REF: Page 245
OBJ: 4-3.1 Using a Table to Write an Equation
NAT: 12.5.2.b
TOP: 4-3 Writing Function Rules
KEY: table | equation | function
4. ANS: D
For a sequence to be an arithmetic sequence, each number subtracted from the one before it should result in a
common difference.
This sequence is arithmetic. Each term differs from the previous one by –6.
Feedback
A
B
C
D
Find the difference between each term and the one before it. If this difference is always
the same, the sequence is arithmetic.
Find the difference between each term and the one before it. If this difference is always
the same, the sequence is arithmetic.
Find the difference between each term and the one before it. If this difference is always
the same, the sequence is arithmetic.
Correct!
PTS: 1
DIF: Average
REF: Page 272
OBJ: 4-6.1 Identifying Arithmetic Sequences
NAT: 12.5.1.a
TOP: 4-6 Arithmetic Sequences
KEY: arithmetic sequence
5. ANS: D
Find a specific term from a given sequence by using the equation
an = your result
a1 = the initial term of the sequence
n = the number in the sequence you want to calculate
d = the common difference between the terms
, where:
n is given in the problem, a1 is the first term in the sequence, and d is the difference between adjacent terms.
Feedback
A
B
C
D
The equation for the nth term contains (n - 1).
Check that the common difference is correct.
Find the correct term in the sequence.
Correct!
PTS: 1
DIF: Average
REF: Page 273
OBJ: 4-6.2 Finding the nth Term of an Arithmetic Sequence
NAT: 12.5.1.a
TOP: 4-6 Arithmetic Sequences
KEY: arithmetic sequence | finding given term | nth term
6. ANS: D
Find the value of the common ratio by dividing each term by the one before it. Then, multiply each term by
the common ratio to get the next term.
Feedback
A
B
First, find the value of the common ratio by dividing each term by the one before it.
Then, multiply each term by the common ratio to get the next term.
Check the signs of the terms.
C
D
Check the order of the terms.
Correct!
PTS: 1
DIF: Basic
REF: Page 766
OBJ: 11-1.1 Extending Geometric Sequences
NAT: 12.5.1.a
TOP: 11-1 Geometric Sequences
7. ANS: C
Find a specific term from a given sequence by using the formula.
, where:
an = your result
a1 = the initial term of the sequence
n = the number in the sequence you want to calculate
r = the common ratio between the terms
Feedback
A
B
C
D
This is the first term raised to the power of the common ratio. Use the formula for the
nth term in a sequence.
The power used in the formula is (n – 1), not (n – 2).
Correct!
The power used in the formula is (n – 1), not (n – 2).
PTS: 1
DIF: Average
REF: Page 767
OBJ: 11-1.2 Finding the nth Term of a Geometric Sequence
NAT: 12.5.1.a
TOP: 11-1 Geometric Sequences
KEY: geometric sequence | nth term
8. ANS: B
Use the equation an = a1 • r n – 1 to solve the problem.
The variables represent the following values:
an = value of the computer after n years
a1 = the initial value of the computer
r = rate of depreciation, 0.5
n = the number of years
Feedback
A
B
C
D
Check that you found the value after the correct number of years.
Correct!
Check that you found the value after the correct number of years.
Check that you found the value after the correct number of years.
PTS:
NAT:
9. ANS:
f(x)
f(6)
f(6)
1
DIF: Average
REF: Page 768
OBJ: 11-1.3 Application
12.5.1.a
TOP: 11-1 Geometric Sequences
KEY: geometric sequence | depreciation
D
=
5,000(0.972)x
Write the function.
=
5,000(0.972)6
Substitute 6 for x.
4,216.65039
Use a calculator to evaluate.

Round your answer to the nearest whole number since the
f(6)
4,217

number of lemmings must be a whole number.
There will be about 4,217 lemmings in 6 years.
Feedback
A
Check your calculation. Use order of operations to determine which operation to do
first.
Check your calculation. Use order of operations to determine which operation to do
first.
Check your calculation. Use order of operations to determine which operation to do
first.
Correct!
B
C
D
PTS: 1
DIF: Average
REF: Page 772
OBJ: 11-2.1 Evaluating an Exponential Function
NAT: 12.5.1.e
TOP: 11-2 Exponential Functions
10. ANS: A
Choose several values of x and generate ordered pairs. Then, graph the ordered pairs and connect with a
smooth curve.
Feedback
A
B
Correct!
The coefficient multiplies the power, it is not added to the power.
PTS: 1
DIF: Basic
REF: Page 773
OBJ: 11-2.3 Graphing y = ab^x with a > 0 and b > 1
NAT: 12.5.1.h
TOP: 11-2 Exponential Functions
KEY: exponential function | graph
11. ANS: B
Make a table. Choose several values of x and generate ordered pairs.
x
y = –(4)x
(x, y)
–1
–1 –(4) = –(0.25) = –0.25
(–1, –0.25)
0
–(4)0 = –(1) = –1
(0, –1)
1
–(4)1 = –(4) = –4
(1, –4)
2
2
–(4) = –(16) = –16
(2, –16)
Graph the ordered pairs and connect them with a smooth curve.
y
5
–4
–3
–2
–1
1
–5
–10
–15
2
3
4
x
Feedback
A
B
Make a table. Substitute values for x into the equation to generate ordered pairs.
Correct!
PTS: 1
DIF: Basic
REF: Page 774
OBJ: 11-2.4 Graphing y = ab^x with a < 0 and b > 1
TOP: 11-2 Exponential Functions
12. ANS: B
Choose some values of x and generate ordered pairs.
NAT: 12.5.1.h
x
0
1
2
Then graph the points and connect with a smooth curve.
Feedback
A
B
The values you found are the opposite of the correct values.
Correct!
PTS: 1
NAT: 12.5.1.h
13. ANS: C
DIF: Average
OBJ: 11-2.5 Graphing y = abx with 0 < b < 1
TOP: 11-2 Exponential Functions
Use the exponential growth equation.
Substitute 105 for a, 0.05 for r, and 11 for t.
Simplify.
Feedback
A
B
C
D
Use the exponential growth equation. Each year the painting is worth (1+ rate) times its
value the previous year.
Convert the rate to a decimal and use the exponential growth equation. Each year the
painting is worth (1+ rate) times its value the previous year.
Correct!
Use the exponential growth equation. Each year the painting is worth (1+ rate) times its
value the previous year.
PTS: 1
DIF: Average
REF: Page 781
OBJ: 11-3.1 Exponential Growth
NAT: 12.5.1.h
TOP: 11-3 Exponential Growth and Decay
14. ANS: B
Use the compound interest formula
. Here, P is 17,400; r is 2.5% expressed as the decimal
0.025; and n is 1 because annually means 1 time per year.
Feedback
A
B
C
D
Express the interest rate in decimal form.
Correct!
The formula has (1+ n/t). Remember to add the 1.
The term n in the exponent should be the number of times per year interest is added.
PTS: 1
DIF: Average
REF: Page 782
OBJ: 11-3.2 Application
NAT: 12.5.1.h
TOP: 11-3 Exponential Growth and Decay
15. ANS: B
Plot the data points and connect them. See whether a line, a parabola, or an exponential curve is the best fit.
This function is exponential.
y
40
30
20
10
–10 –8
–6
–4
–2
–10
2
4
6
8
10
x
–20
–30
–40
Feedback
A
B
C
D
Graph the points. Does a line, a parabola, or an exponential curve best fit the data?
Correct!
Graph the points. Does a line, a parabola, or an exponential curve best fit the data?
Graph the points. Does a line, a parabola, or an exponential curve best fit the data?
PTS: 1
DIF: Basic
REF: Page 789
OBJ: 11-4.1 Graphing Data to Choose a Model
NAT: 12.5.2.g
TOP: 11-4 Linear Quadratic and Exponential Models
KEY: model | data | linear | exponential | quadratic
16. ANS: A
Check for a pattern in the differences and the ratios of the y-terms.
A linear function has constant first differences.
A quadratic function has constant second differences.
A cubic function has constant third differences.
An exponential function has constant ratios.
Change in
Time
Population Growth of
Bacteria
Time
Number of
(hours)
Bacteria
0
2,000
First
Difference
Second
Difference
Ratio
1
1
1
1
1
2
3
4
5,000
12,500
31,250
78,125
3,000
7,500
18,750
46,875
4,500
11,250
28,125
2.5
2.5
2.5
2.5
For each change in time of 1 hour, only the ratios of the y-terms remain constant.
The best model for the data is an exponential function.
Feedback
A
B
C
D
Correct!
Check the differences and the ratios. Cubic functions have constant third differences.
Check the differences and the ratios. Quadratic functions have constant second
differences.
Check the differences and the ratios. Linear functions have constant first differences.
PTS: 1
DIF: Average
REF: Page 790
OBJ: 11-4.2 Using Patterns to Choose a Model
TOP: 11-4 Linear Quadratic and Exponential Models
17. ANS:
NAT: 12.5.2.g
–
18.
19.
20.
21.
22.
23.
24.
PTS:
TOP:
KEY:
NOT:
ANS:
TOP:
BLM:
ANS:
TOP:
BLM:
ANS:
TOP:
BLM:
ANS:
TOP:
BLM:
ANS:
TOP:
BLM:
ANS:
TOP:
BLM:
ANS:
1
DIF: Level B
REF: MALG1139
Lesson 8.3 Define and Use Zero and Negative Exponents
rewrite | positive exponents | expression
BLM: Comprehension
978-0-618-65612-7
A
PTS: 1
DIF: Level A
REF: MALG1158
Lesson 8.4 Use Scientific Notation KEY: scientific notation
Knowledge NOT: 978-0-618-65612-7
D
PTS: 1
DIF: Level A
REF: MALG1160
Lesson 8.4 Use Scientific Notation KEY: scientific notation
Knowledge NOT: 978-0-618-65612-7
A
PTS: 1
DIF: Level B
REF: MALG1174
Lesson 8.4 Use Scientific Notation KEY: multiply | product | scientific notation
Comprehension
NOT: 978-0-618-65612-7
C
PTS: 1
DIF: Level B
REF: MALG1178
Lesson 8.4 Use Scientific Notation KEY: word | scientific notation
Application NOT: 978-0-618-65612-7
B
PTS: 1
DIF: Level A
REF: MALG1194
Lesson 8.4 Use Scientific Notation KEY: scientific notation
Application NOT: 978-0-618-65612-7
C
PTS: 1
DIF: Level B
REF: MALG0256
Lesson 8.4 Use Scientific Notation KEY: order | scientific notation | compare
Knowledge NOT: 978-0-618-65612-7
PTS: 1
DIF: Level A
KEY: scientific notation
REF: MALG1157
BLM: Knowledge
TOP: Lesson 8.4 Use Scientific Notation
NOT: 978-0-618-65612-7
25. ANS:
PTS: 1
DIF: Level A
KEY: scientific notation
26. ANS:
0.0000000315
REF: MALG1162
BLM: Knowledge
TOP: Lesson 8.4 Use Scientific Notation
NOT: 978-0-618-65612-7
PTS: 1
DIF: Level A
KEY: scientific notation | decimal form
27. ANS:
3,940,000,000
REF: MALG1165
BLM: Knowledge
TOP: Lesson 8.4 Use Scientific Notation
NOT: 978-0-618-65612-7
PTS: 1
DIF: Level A
KEY: decimal form | scientific notation
28. ANS:
350
REF: MALG1166
BLM: Knowledge
TOP: Lesson 8.4 Use Scientific Notation
NOT: 978-0-618-65612-7
PTS:
KEY:
NOT:
29. ANS:
TOP:
KEY:
30. ANS:
TOP:
KEY:
31. ANS:
1
DIF: Level B
REF: MALG1173 TOP:
scientific notation | multiply | decimal form
BLM:
978-0-618-65612-7
D
PTS: 1
DIF: Level B
REF:
Lesson 8.5 Write and Graph Exponential Growth Functions
word | log | compound interest
BLM: Application NOT:
B
PTS: 1
DIF: Level B
REF:
Lesson 8.5 Write and Graph Exponential Growth Functions
law of exponents | word
BLM: Application NOT:
Lesson 8.4 Use Scientific Notation
Comprehension
MAL21007
978-0-618-65612-7
MAL21020
978-0-618-65612-7
PTS: 1
DIF: Level B
REF: MALG1201
TOP: Lesson 8.5 Write and Graph Exponential Growth Functions
KEY: graph | exponential
BLM: Knowledge NOT: 978-0-618-65612-7
32. ANS:
$1967.15
PTS: 1
DIF: Level B
REF: MAL21013
TOP: Lesson 8.5 Write and Graph Exponential Growth Functions
KEY: compound interest
BLM: Application NOT: 978-0-618-65612-7
33. ANS:
$666.34
PTS: 1
DIF: Level B
REF: MAL21017
TOP: Lesson 8.5 Write and Graph Exponential Growth Functions
KEY: compound interest
BLM: Application NOT: 978-0-618-65612-7
34. ANS:
A rule for the function is
PTS:
TOP:
KEY:
NOT:
35. ANS:
1
DIF: Level B
REF: A1.08.05.FR.07
Lesson 8.5 Write and Graph Exponential Growth Functions
free response | function | exponential
BLM: Comprehension
978-0-618-65612-7
PTS: 1
DIF: Level B
REF: 7ef48cae-cdbb-11db-b502-0011258082f7
TOP: Lesson 8.5 Write and Graph Exponential Growth Functions
KEY: Exponential growth
BLM: Knowledge NOT: 978-0-618-65612-7
36. ANS:
exponential decay
PTS:
TOP:
KEY:
NOT:
37. ANS:
1
DIF: Level B
REF: MALG1207
Lesson 8.6 Write and Graph Exponential Decay Functions
graph | exponential | growth | decay
BLM: Comprehension
978-0-618-65612-7
y
5
–5
5
x
–5
exponential growth
PTS:
TOP:
KEY:
NOT:
38. ANS:
a.
1
DIF: Level B
REF: MALG1208
Lesson 8.6 Write and Graph Exponential Decay Functions
graph | exponential | growth | decay
BLM: Comprehension
978-0-618-65612-7
PTS: 1
DIF: Level A
REF: MALG1209
TOP: Lesson 8.6 Write and Graph Exponential Decay Functions
KEY: determine | exponential decay
BLM: Knowledge NOT: 978-0-618-65612-7
39. ANS:
y
5
–5
5
x
–5
exponential decay
PTS: 1
DIF: Level B
REF: MALG1212
TOP: Lesson 8.6 Write and Graph Exponential Decay Functions
KEY: graph | exponential | growth | decay
BLM: Comprehension
NOT: 978-0-618-65612-7
40. ANS:
1.99 yr
PTS: 1
DIF: Level B
REF: MALG1213
TOP: Lesson 8.6 Write and Graph Exponential Decay Functions
KEY: exponent | radioactive decay | log
BLM: Application NOT: 978-0-618-65612-7
41. ANS:
2152
PTS:
TOP:
KEY:
NOT:
42. ANS:
1
DIF: Level B
REF: MALG1215
Lesson 8.6 Write and Graph Exponential Decay Functions
write | solve | word | exponential equation
BLM: Comprehension
978-0-618-65612-7
Exponential decay;
or
PTS: 1
DIF: Level B
REF: 7ef66203-cdbb-11db-b502-0011258082f7
TOP: Lesson 8.6 Write and Graph Exponential Decay Functions
KEY: Exponential growth | exponential decay
BLM: Knowledge
NOT: 978-0-618-65612-7
43. ANS:
Exponential growth;
PTS:
TOP:
KEY:
NOT:
44. ANS:
1
DIF: Level B
REF: 7ef77408-cdbb-11db-b502-0011258082f7
Lesson 8.6 Write and Graph Exponential Decay Functions
Exponential growth | exponential decay
BLM: Knowledge
978-0-618-65612-7
The graph of
PTS:
TOP:
KEY:
NOT:
45. ANS:
is a vertical shrink of
.
1
DIF: Level A
REF: 7ef9495d-cdbb-11db-b502-0011258082f7
Lesson 8.6 Write and Graph Exponential Decay Functions
Exponential growth | exponential decay
BLM: Knowledge
978-0-618-65612-7
The graph of
PTS:
TOP:
KEY:
NOT:
47. ANS:
TOP:
KEY:
48. ANS:
with a reflection in the x -axis.
1
DIF: Level A
REF: 7ef9224d-cdbb-11db-b502-0011258082f7
Lesson 8.6 Write and Graph Exponential Decay Functions
Exponential growth | exponential decay
BLM: Knowledge
978-0-618-65612-7
The graph of
PTS:
TOP:
KEY:
NOT:
46. ANS:
is a vertical stretch of
is a reflection in the x-axis of
.
1
DIF: Level A
REF: 7ef9706d-cdbb-11db-b502-0011258082f7
Lesson 8.6 Write and Graph Exponential Decay Functions
Exponential growth | exponential decay
BLM: Knowledge
978-0-618-65612-7
D
PTS: 1
DIF: Level B
REF: MALG1096
Lesson 8.1 Apply Exponent Properties Involving Products
exponent
BLM: Knowledge NOT: 978-0-618-65612-7
A
PTS: 1
DIF: Level B
REF: MALG1102
49.
50.
51.
52.
53.
54.
TOP:
KEY:
NOT:
ANS:
TOP:
KEY:
ANS:
TOP:
KEY:
NOT:
ANS:
TOP:
KEY:
NOT:
ANS:
TOP:
KEY:
NOT:
ANS:
TOP:
KEY:
ANS:
Lesson 8.1 Apply Exponent Properties Involving Products
simplify | exponent | multiply | product rule
BLM:
978-0-618-65612-7
A
PTS: 1
DIF: Level A
REF:
Lesson 8.1 Apply Exponent Properties Involving Products
simplify | power rule | exponent
BLM: Knowledge NOT:
D
PTS: 1
DIF: Level A
REF:
Lesson 8.1 Apply Exponent Properties Involving Products
variable | exponent | power | power to a power
BLM:
978-0-618-65612-7
D
PTS: 1
DIF: Level B
REF:
Lesson 8.1 Apply Exponent Properties Involving Products
polynomial | exponent
BLM: Comprehension
978-0-618-65612-7
B
PTS: 1
DIF: Level B
REF:
Lesson 8.1 Apply Exponent Properties Involving Products
simplify | power rule | exponent
BLM: Comprehension
978-0-618-65612-7
A
PTS: 1
DIF: Level A
REF:
Lesson 8.2 Apply Exponent Properties Involving Quotients
exponents | divide
BLM: Knowledge NOT:
Knowledge
MALG1104
978-0-618-65612-7
MALG1117
Knowledge
MALG1112
MALG1110
MALG1122
978-0-618-65612-7
PTS:
TOP:
KEY:
BLM:
55. ANS:
125
1
DIF: Level B
REF: MALG1126
Lesson 8.2 Apply Exponent Properties Involving Quotients
fraction | simplify | monomial | exponent law | exponent | power | quotient
Knowledge NOT: 978-0-618-65612-7
PTS:
TOP:
KEY:
56. ANS:
TOP:
KEY:
57. ANS:
TOP:
KEY:
58. ANS:
1
DIF: Level B
REF: MALG1124
Lesson 8.2 Apply Exponent Properties Involving Quotients
add | evaluate | exponent | subtract BLM: Knowledge NOT:
A
PTS: 1
DIF: Level B
REF:
Lesson 8.3 Define and Use Zero and Negative Exponents
negative | exponent
BLM: Knowledge NOT:
B
PTS: 1
DIF: Level A
REF:
Lesson 8.3 Define and Use Zero and Negative Exponents
zero | exponent | multiply
BLM: Knowledge NOT:
1
PTS:
TOP:
KEY:
NOT:
59. ANS:
–5
1
DIF: Level A
REF: MALG1155
Lesson 8.3 Define and Use Zero and Negative Exponents
exponent | power | additive inverse | zero
BLM: Knowledge
978-0-618-65612-7
978-0-618-65612-7
MALG1134
978-0-618-65612-7
MALG1131
978-0-618-65612-7
PTS:
TOP:
KEY:
60. ANS:
1
DIF: Level A
REF: MALG1132
Lesson 8.3 Define and Use Zero and Negative Exponents
evaluate | exponent | zero
BLM: Knowledge NOT: 978-0-618-65612-7
120
PTS: 1
61. ANS: 5
DIF: Advanced
NAT: 12.5.1.a
TOP: 11-1 Geometric Sequences
PTS: 1
62. ANS:
DIF: Average
TOP: 11-2 Exponential Functions
PTS: 1
DIF: Level B
REF: MALG1133
TOP: Lesson 8.3 Define and Use Zero and Negative Exponents
KEY: negative exponent
BLM: Knowledge NOT: 978-0-618-65612-7
63. ANS:
PTS:
TOP:
KEY:
NOT:
64. ANS:
1
DIF: Level B
REF: MALG1135
Lesson 8.3 Define and Use Zero and Negative Exponents
rewrite | positive exponents | expression
BLM: Knowledge
978-0-618-65612-7
PTS: 1
DIF: Level B
REF: MALG1136
TOP: Lesson 8.3 Define and Use Zero and Negative Exponents
KEY: expression | rewrite | positive exponents
BLM: Comprehension
NOT: 978-0-618-65612-7
65. ANS: D
Find a specific term from a given sequence by using the equation below.
, where:
an = your result
a1 = the initial term of the sequence
n = the number in the sequence you want to calculate
d = the common difference between the terms
n is stated in the problem, a1 is the first term in the sequence, and d is the difference between adjacent terms.
Feedback
A
B
Remember that the equation for the nth term contains (n - 1).
Make sure you are finding the proper term in the sequence.
C
D
Check that you found the common difference correctly.
Correct!
PTS: 1
DIF: Average
REF: Page 684
OBJ: 13-1.2 Finding a Given Term of an Arithmetic Sequence NAT: 8.5.1.a
STA: M8A3.e
TOP: 13-1 Terms of Arithmetic Sequences
KEY: arithmetic sequence
66. ANS: D
If the list is a geometric sequence, each number divided by the one before it should result in a common ratio.
Feedback
A
B
C
D
A geometric sequence has a consistent ratio between the terms .
Check the sign of your ratio.
Check that you found the common ratio correctly.
Correct!
PTS: 1
DIF: Basic
REF: Page 687
OBJ: 13-2.1 Identifying Geometric Sequences
NAT: 8.5.1.a
TOP: 13-2 Terms of Geometric Sequences
KEY: geometric sequence
67. ANS: C
Find a specific term from a given sequence by using the equation below.
, where:
an = your result
a1 = the initial term of the sequence
n = the number in the sequence you want to calculate
r = the common ratio between the terms
Feedback
A
B
C
D
Check the sign of your common ratio.
Remember that (n - 1), not n, is the power used in the formula.
Correct!
Did you remember all the parts of the equation?
PTS: 1
DIF: Average
REF: Page 688
OBJ: 13-2.2 Finding a Given Term of a Geometric Sequence
NAT: 8.5.1.a
STA: M8N1.i
TOP: 13-2 Terms of Geometric Sequences
KEY: geometric sequence
68. ANS: A
To graph a function, create a table of data points. Plot these points. Consider the equation
Using the values –2 to 2 for x, you can calculate the following table of values:
x
–2
–1
0
1
2
y
0.75
1.5
3
6
12
.
When plotted, the points produce the following graph:
y
9
8
7
6
5
4
3
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
x
Feedback
A
B
Correct!
Should the y-values be increasing or decreasing as x increases?
PTS: 1
DIF: Basic
REF: Page 704
OBJ: 13-5.1 Graphing Exponential Functions
NAT: 8.5.2.g
STA: M8A3.i
TOP: 13-5 Exponential Functions
KEY: exponential function | graph
69. ANS:
a. Yes
b. Any sequence of identical digits, for example, 2, 2, 2, 2, 2, ...
Scoring Rubric:
4
The solution is correct, and all of the work is shown as above.
or
A different logical method is used to find the correct solution.
3
Both solutions are correct, but not all of the work is shown.
2
The solution for part a is correct, but the solution for part b is incorrect.
or
The solution for part a is incorrect, but the work for part b is correct.
1
Both solutions are incorrect, and the work shows no understanding of the concept.
PTS: 1
DIF: Average
NAT: 8.5.1.a
TOP: 13-2 Terms of Geometric Sequences
KEY: geometric sequence