Download Ch. 6 Unit Assignment

Name: ______________________
Class: _________________
Date: _________
Ch. 6 Unit Assignment
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. How many x-intercepts does the exponential function f(x) = 2(10)x have?
A.
B.
C.
D.
____
2. Match the following graph with its function.
A.
B.
C.
D.
____
0
1
2
3
y = 3(0.5)x
y = 2(1.25)x
y = 0.5(3)x
y = 2(0.75)x
1 x
3. Determine the y-intercept of the exponential function f(x) = 4( ) .
2
A.
B.
C.
D.
0
1
2
4
1
ID: A
Name: ______________________
____
4. Express (
A.
B.
C.
D.
____
32 )
2x
ID: A
as a power with a base of 2.
5x
2
10x
2
2.5x
2
20x
2
5. Solve the following exponential equation by writing both sides with the same base.
4a
3 = 243
3
4
5
B. a =
8
9
C. a =
16
7
D. a =
8
A. a =
____
6. The following data set involves exponential growth. Determine the missing value from the table.
x
0
1
2
3
4
5
6
y
0.16
0.40
1.00
2.50
15.63
39.06
A.
B.
C.
D.
____
6.25
5.00
7.50
8.75
7. Determine the equation of the exponential regression function for the data.
x
0
1
2
3
4
5
y
3.5
5.6
9.0
14.2
23.1
36.7
A.
B.
C.
D.
y = 3.5(1.6)x
y = 2.2(1.6)x
y = 3.5(1.8)x
y = 3.5(0.8)x
2
Name: ______________________
____
ID: A
8. A scatter plot is drawn using a data set.
Extrapolate the value of y when x = 10.
A.
B.
C.
D.
____
9. The equation of the exponential function that models a data set is
y = 78.20(0.87)x
Interpolate the value of y when x = 5.5.
A.
B.
C.
D.
____
1.5
–0.3
0.0
1.0
36.35
46.49
22.50
38.98
10. An investment can be modelled by the following growth function, where x represents the time in
years:
y = 2500(1.018)x
What was the principal invested?
A.
B.
C.
D.
$1250
$2500
$18
$1018
3
Name: ______________________
____
11. An investment can be modelled by the following growth function, where x represents the time in
years:
y = 4800(1.03)x
How long, in months, did it take for the account to reach $5000?
A.
B.
C.
D.
____
ID: A
1
9
13
17
12. Solve the following investment equation for the number of compounding periods, n. Round your
answer to the nearest whole number.
350 = 300(1.04)n
A.
B.
C.
D.
2
4
8
16
Short Answer
1. Complete the table of values for the function g(x) = 3(
x
–3
–2
–1
0
1
2
3
g(x)
4
1 x
) . (2 marks)
10
Name: ______________________
ID: A
2. For the exponential function shown, estimate the x-values at y = 4 and y = 3. (2 marks)
3. Solve the following exponential equation by writing both sides with the same base. (1 mark)
2a − 1
1000 = 10
.
4. Determine whether the following data set involves exponential growth, exponential decay, or
neither. Explain how you know. (2 marks)
x
1
2
3
4
5
6
y
5
15
45
135
405
1215
.
5
Name: ______________________
ID: A
5. The fish population in Loon Lake is modelled by the equation
P(t) = 2500(0.92)t
where P(t) represents the number of fish and t represents the time, in years, since 2010.
Estimate the fish population in 2030. (1 mark)
.
Problem
1. A vehicle was purchased for $15 000 in 2005. The book value of the vehicle can be modelled by the
exponential function
x
y = 15 000 (0.82)
where y represents the value in dollars and x represents the time, in years, after 2005.
a) How does the value of the vehicle change over time? Explain how you know. (2 marks)
b) Estimate the value of the vehicle in 2015. Show your work. (1 mark)
.
2. Solve the equation and verify your answer by substitution. Show your work. ( 2 marks)
5−x
6 (8)
= 3072
.
6
Name: ______________________
ID: A
3. Thorium-227 has a half-life of 18.4 days. The remaining amount of a 50-mg sample of thorium-227
can be modelled by the equation
t
1 18.4
A(t) = 50( )
2
where A(t) is the amount of thorium-227 remaining, in milligrams, and t is the time in days.
a) Determine when 12.5 mg of thorium-227 are remaining. Show your work. (1 mark)
b) Use a graphing calculator to determine when 5 mg of thorium-227 are remaining, to the nearest
day. Show your work. (1 mark)
7
ID: A
Ch. 6 Unit Assignment
Answer Section
MULTIPLE CHOICE
1. ANS: A
PTS: 1
DIF: Grade 12
REF: Lesson 6.1
OBJ: 6.1 Describe, orally and in written form, the characteristics of an exponential or logarithmic
function by analyzing its graph.
TOP: Exploring the characteristics of exponential functions
KEY: exponential function
2. ANS: B
PTS: 1
DIF: Grade 12
REF: Lesson 6.2
OBJ: 6.1 Describe, orally and in written form, the characteristics of an exponential or logarithmic
function by analyzing its graph. | 6.2 Describe, orally and in written form, the characteristics of an
exponential or logarithmic function by analyzing its equation. | 6.3 Match equations in a given set
to their corresponding graphs.
TOP: Relating the characteristics of an exponential function to its equation
KEY: exponential function
3. ANS: D
PTS: 1
DIF: Grade 12
REF: Lesson 6.2
OBJ: 6.1 Describe, orally and in written form, the characteristics of an exponential or logarithmic
function by analyzing its graph. | 6.2 Describe, orally and in written form, the characteristics of an
exponential or logarithmic function by analyzing its equation. | 6.3 Match equations in a given set
to their corresponding graphs.
TOP: Relating the characteristics of an exponential function to its equation
KEY: exponential function
4. ANS: A
PTS: 1
DIF: Grade 12
REF: Lesson 6.3
OBJ: 5.1 Determine the solution of an exponential equation in which the bases are powers of one
another. | 5.2 Determine the solution of an exponential equation in which the bases are not powers
of one another.
TOP: Solving exponential equations
KEY: exponential function
5. ANS: B
PTS: 1
DIF: Grade 12
REF: Lesson 6.3
OBJ: 5.1 Determine the solution of an exponential equation in which the bases are powers of one
another. | 5.2 Determine the solution of an exponential equation in which the bases are not powers
of one another.
TOP: Solving exponential equations
KEY: exponential function
6. ANS: A
PTS: 1
DIF: Grade 12
REF: Lesson 6.4
OBJ: 6.4 Graph data and determine the exponential or logarithmic function that best
approximates the data. | 6.5 Interpret the graph of an exponential or logarithmic function that
models a situation, and explain the reasoning. | 6.6 Solve, using technology, a contextual problem
that involves data that is best represented by graphs of exponential or logarithmic functions, and
explain the reasoning.
TOP: Modelling data using exponential functions
KEY: exponential function
1
ID: A
7. ANS: A
PTS: 1
DIF: Grade 12
REF: Lesson 6.4
OBJ: 6.4 Graph data and determine the exponential or logarithmic function that best
approximates the data. | 6.5 Interpret the graph of an exponential or logarithmic function that
models a situation, and explain the reasoning. | 6.6 Solve, using technology, a contextual problem
that involves data that is best represented by graphs of exponential or logarithmic functions, and
explain the reasoning.
TOP: Modelling data using exponential functions
KEY: exponential function | regression function
8. ANS: D
PTS: 1
DIF: Grade 12
REF: Lesson 6.4
OBJ: 6.4 Graph data and determine the exponential or logarithmic function that best
approximates the data. | 6.5 Interpret the graph of an exponential or logarithmic function that
models a situation, and explain the reasoning. | 6.6 Solve, using technology, a contextual problem
that involves data that is best represented by graphs of exponential or logarithmic functions, and
explain the reasoning.
TOP: Modelling data using exponential functions
KEY: exponential function | regression function | interpolate
9. ANS: A
PTS: 1
DIF: Grade 12
REF: Lesson 6.4
OBJ: 6.4 Graph data and determine the exponential or logarithmic function that best
approximates the data. | 6.5 Interpret the graph of an exponential or logarithmic function that
models a situation, and explain the reasoning. | 6.6 Solve, using technology, a contextual problem
that involves data that is best represented by graphs of exponential or logarithmic functions, and
explain the reasoning.
TOP: Modelling data using exponential functions
KEY: exponential function | regression function | interpolate
10. ANS: B
PTS: 1
DIF: Grade 12
REF: Lesson 6.5
OBJ: 5.1 Determine the solution of an exponential equation in which the bases are powers of one
another. | 5.2 Determine the solution of an exponential equation in which the bases are not powers
of one another. | 5.3 Solve problems that involve the application of exponential equations to loans,
mortgages and investments.
TOP: Financial applications involving exponential functions
KEY: exponential function | principal
11. ANS: D
PTS: 1
DIF: Grade 12
REF: Lesson 6.5
OBJ: 5.1 Determine the solution of an exponential equation in which the bases are powers of one
another. | 5.2 Determine the solution of an exponential equation in which the bases are not powers
of one another. | 5.3 Solve problems that involve the application of exponential equations to loans,
mortgages and investments.
TOP: Financial applications involving exponential functions
KEY: exponential function
12. ANS: B
PTS: 1
DIF: Grade 12
REF: Lesson 6.5
OBJ: 5.1 Determine the solution of an exponential equation in which the bases are powers of one
another. | 5.2 Determine the solution of an exponential equation in which the bases are not powers
of one another. | 5.3 Solve problems that involve the application of exponential equations to loans,
mortgages and investments.
TOP: Financial applications involving exponential functions
KEY: exponential function | compounding period
2
ID: A
SHORT ANSWER
1. ANS:
x
–3
–2
–1
0
1
2
3
g(x)
−3
ˆ
Ê 1 ˜
˜
3Á
= 3000
˜
˜
10
˜
Ë
˜
˜
¯ −2
˜
ˆ
Ê 1 ˜
˜
˜
3Á
= 300
˜
˜
10
˜
Ë
˜
˜
¯
˜ −1
Ê 1 ˆ
˜
˜
3Á
= 30
˜
˜
10
˜
Ë
˜
˜
¯0
˜
ˆ
Ê 1 ˜
˜
˜
3Á
=3
˜
˜
10
˜
Ë
˜
˜
¯
˜1
Ê 1 ˆ
˜
˜
3Á
= 0.3
˜
˜
10
˜
Ë
˜
˜
¯2
˜
ˆ
Ê 1 ˜
˜
˜
3Á
= 0.03
˜
˜
10
˜
Ë
˜
˜
¯
˜3
ˆ
Ê 1 ˜
˜
˜
3Á
= 0.003
˜
˜
10
˜
Ë
˜
˜
¯
˜
PTS: 1
DIF: Grade 12
REF: Lesson 6.1
OBJ: 6.1 Describe, orally and in written form, the characteristics of an exponential or logarithmic
function by analyzing its graph.
TOP: Exploring the characteristics of exponential functions
KEY: exponential function
2. ANS:
x = –4; x = –3.6
PTS: 1
DIF: Grade 12
REF: Lesson 6.3
OBJ: 5.1 Determine the solution of an exponential equation in which the bases are powers of one
another. | 5.2 Determine the solution of an exponential equation in which the bases are not powers
of one another.
TOP: Solving exponential equations
KEY: exponential function
3
ID: A
3. ANS:
5
a=
4
PTS: 1
DIF: Grade 12
REF: Lesson 6.3
OBJ: 5.1 Determine the solution of an exponential equation in which the bases are powers of one
another. | 5.2 Determine the solution of an exponential equation in which the bases are not powers
of one another.
TOP: Solving exponential equations
KEY: exponential function
4. ANS:
Exponential growth; the y-values are tripling for every increase in the x-value.
PTS: 1
DIF: Grade 12
REF: Lesson 6.4
OBJ: 6.4 Graph data and determine the exponential or logarithmic function that best
approximates the data. | 6.5 Interpret the graph of an exponential or logarithmic function that
models a situation, and explain the reasoning. | 6.6 Solve, using technology, a contextual problem
that involves data that is best represented by graphs of exponential or logarithmic functions, and
explain the reasoning.
TOP: Modelling data using exponential functions
KEY: exponential function
5. ANS:
472
PTS: 1
DIF: Grade 12
REF: Lesson 6.4
OBJ: 6.4 Graph data and determine the exponential or logarithmic function that best
approximates the data. | 6.5 Interpret the graph of an exponential or logarithmic function that
models a situation, and explain the reasoning. | 6.6 Solve, using technology, a contextual problem
that involves data that is best represented by graphs of exponential or logarithmic functions, and
explain the reasoning.
TOP: Modelling data using exponential functions
KEY: exponential function | regression function
4
ID: A
PROBLEM
1. ANS:
a) The value is decreasing because the constant term is positive and the base is between 0 and 1.
b) 2015 is ten years after 2005, so x = 10:
x
y = 15 000 (0.82)
10
y = 15 000 (0.82)
y = 2061.720. . .
The value of the vehicle in 2015 is about $2061.72.
PTS: 1
DIF: Grade 12
REF: Lesson 6.2
OBJ: 6.1 Describe, orally and in written form, the characteristics of an exponential or logarithmic
function by analyzing its graph. | 6.2 Describe, orally and in written form, the characteristics of an
exponential or logarithmic function by analyzing its equation. | 6.3 Match equations in a given set
to their corresponding graphs.
TOP: Relating the characteristics of an exponential function to its equation
KEY: exponential function
5
ID: A
2. ANS:
Rewrite both sides as powers of 8:
5−x
6 (8)
= 3072
1
5−x
1
× 6 (8)
= × 3072
6
6
5−x
8
= 512
5−x
3
8
=8
Since the bases on both sides are both 8, the exponents must also be equal:
5−x= 3
5−3 = x
x=2
Verify x = 2:
LS
RS
5−x
3072
6 (8)
5−2
6 (8)
3
6 (8)
6 × 512
3072
LS = RS
PTS: 1
DIF: Grade 12
REF: Lesson 6.3
OBJ: 5.1 Determine the solution of an exponential equation in which the bases are powers of one
another. | 5.2 Determine the solution of an exponential equation in which the bases are not powers
of one another.
TOP: Solving exponential equations
KEY: exponential function
6
ID: A
3. ANS:
a) Rewrite both sides as powers of
1
:
2
t
˜ 18.4
Ê 1ˆ
˜
12.5 = 50 Á ˜
˜
Ë 2˜
˜
˜
¯
˜
t
18.4
ˆ
˜
Ê
1
1
1˜
× 12.5 =
× 50 Á ˜
˜
50
50
˜
Ë 2˜
˜
˜
¯
˜
t
18.4
ˆ
Ê 1˜
1
˜
= Á ˜
˜
4
Ë 2˜
˜
˜
¯ t
˜
2
18.4
ˆ
ˆ
Ê 1˜
Ê 1˜
˜
˜
˜
˜
=
Á2˜
Á2˜
˜
˜
Ë ˜
Ë ˜
˜
˜
˜
˜
¯
¯
˜
Since the bases on˜both sides are both are the same, the exponents must also be equal:
t
2=
18.4
t = 2(18.4)
t = 36.8
After 36.8 days, 12.5 mg of thorium-227 are remaining.
b) Use a graphing calculator to create a system of equations:
y1 = 5
x
˜ 18.4
Ê 1ˆ
˜
y2 = 50 Á ˜
˜
Ë 2˜
˜
˜
¯
˜
The x-coordinate of the point of intersection is the solution to the exponential equation
ˆ
Ê 1˜
˜
5 = 50 Á ˜
˜
˜
Ë 2˜
˜
˜
¯
˜
x
18.4
.
After 61 days, 5 mg of thorium-227 are remaining.
7
ID: A
PTS: 1
DIF: Grade 12
REF: Lesson 6.3
OBJ: 5.1 Determine the solution of an exponential equation in which the bases are powers of one
another. | 5.2 Determine the solution of an exponential equation in which the bases are not powers
of one another.
TOP: Solving exponential equations
KEY: exponential function | half-life
8