Unit 8 Application and Thinking Review
Name:_______________________
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. State the transformations, in proper order, that are needed to turn
into
a)
reflection in the x-axis, vertical compression of , vertical translation 7 units up.
.
b) reflection in the y-axis, vertical stretch by 2, vertical translation 5 units up.
c)
vertical translation 5 units down, vertical compression of , reflection in the x-axis.
d)
reflection in the x-axis, vertical translation 5 units down, vertical compression of
.
____
2. The function
has the point (10, 1) on its graph. Find the coordinates of the image point
transformed from (10, 1) on the transformed function
.
a) ( 2 , 4 )
c) ( 14 , 5 )
b) ( 2 , 5 )
d) ( 4 , 5 )
____
3. Which of the following functions results if
is vertically stretched by 4, horizontally stretched by
3, reflected in the y-axis, horizontally translated 5 units to the right and vertically translated 2 units up?
a)
c)
b)
d)
____
4. Which of the following characteristics of the function
changes under the following
transformations:
?
a) The range of the function
c) The x-intercept
b) The domain of the function
d) The vertical asymptote
____
5. The population of bacteria in a Petri dish increases by a factor of 10 every hour. If there are initially 20
bacteria in the dish, how long will it take before the population increases to 60 000 to the nearest tenth of an
hour?
a) 3000.0 h
c) 4.8 h
b) 300.0 h
d) 3.5 h
____
6. Which of the following is not a strategy for solving simple exponential equations?
a) Express both sides as powers with a common base and then equate the exponents.
b) Divide both sides by the common base and compare the exponents
c) Graph both sides of the equation using graphing technology and then determine the point
of intersection.
d) Rewrite the equation in logarithmic form and simplify.
____
7. A certain radioactive isotope has a half life of 5 years. If a sample has 120 grams of radioactive material,
what equation could be used to determine the amount of material remaining (y) after x years.
a)
c)
b)
d)
____
8. Which of the following statements will NOT be true regarding the graphs of
?
a)
b)
c)
d)
____
They will all have the same vertical asymptote
The will all have the same x-intercept
They will all curve in the same direction
They will all have the same domain
9. Solve for x.
a) 20
b) 89
____ 10. Write
a)
.
c) 120
d) 1600
as a single logarithm.
c)
b)
____ 11. Which of the following statements is correct?
a)
b)
d)
c)
d)
____ 12. Which of the following equations could be used when solving
a)
c)
b)
d)
?
____ 13. Which of the following statements is NOT true?
a) Two exponential expressions with the same base are equal when their exponents are equal.
b) If two expressions are equal, taking the log of both expressions maintains their equality.
c) Sometimes an exponential equation can be solved algebraically by writing both sides of
the equation to the same base, setting the exponents equal to each other, and solving for
the unknown.
d) If two exponential expressions are equal, doubling the base of both expressions maintains
their equality.
____ 14. If $800 is deposited into an account that pays 6 % / a compounded monthly, how many months will it take the
investment to grow to $2000?
a) 48
c) 188
b) 184
d) 333
____ 15. The half-life of a certain substance is 5.9 days. How many days will it take for 30 g of the substance to decay
to 12 g?
a) 1.3
c) 7.8
b) 2.5
d) 18
____ 16. Which of the following is a valid reason for using common logarithms when solving an exponential equation
algebraically?
a) Common logarithms can be easily evaluated using readily available technologies.
b) Taking any log other than the common log of two equal expressions does not maintain
their equality.
c) Common logs more closely model the base 10 system than all other logs.
d) The power, product and quotient laws of logarithms apply only to common logs.
____ 17. Which of the following is NOT a strategy that is often used to solve logarithmic equations?
a) Express the equation in exponential form and solve the resulting exponential equation.
b) Simplify the expressions in the equation by using the laws of logarithms.
c) Represent the sums or differences of logs as single logarithms.
d) Square all logarithmic expressions and solve the resulting quadratic equation.
____ 18. Given that the loudness, L, of a sound in decibels (dB) can be calculated using the formula
where I is the intensity of the sound in watts per square metre
and
,
, determine the
intensity of the sound of an audience applauding if the sound level is 150 dB.
a) 100
c) 10000
b) 1000
d) 14.18
____ 19. Describe the strategy you would use to solve
.
a) Use the product rule to turn the right side of the equation into a single logarithm.
Recognize that the resulting value is equal to x.
b) Express the equation in exponential form, set the exponents equal to each other and solve.
c) Use the fact that the logs have the same base to add the expressions on the right side of the
equation together. Express the results in exponential form, set the exponents equal to each
other and solve.
d) Use the fact that since both sides of the equations have logarithms with the same base to
set the expressions equal to each other and solve.
____ 20. Given the formula for magnitude of an earthquake,
amplitude a is in an earthquake with
a) 1.2 times as large
b) 1.6 times as large
, determine the how many times larger the
compared to one with
c) 9.4 times as large
d) 15.8 times as large
____ 21. The sound level of a dog barking is 83 dB. The sound level of a thunder clap is 102 dB. How many times
louder is the thunder clap than the dog?
a) 1.23
c) 79.43
b) 19
d) 8499
____ 22. Which of the following Richter scale measurements represent a earthquake with approximately twice the
intensity of tremor measuring 3.5?
a) 3.8
c) 7.0
b) 4.5
d) 12.25
____ 23. How long will it take for $5000 to accumulate to $8000 if it is invested at an interest rate of 7.5%/a
compounded annually?
a) 1.6 years
c) 6.5 years
b) 5.4 years
d) 8 years
____ 24. A sound measures 42 dB. The intensity of a second sound is four times as great. What is the decibel level of
this second sound?
a) 48.02
c) 84.06
b) 168
d) 63.78
____ 25. Every time a fluid is purified using a certain method of evaporation and condensation, 3.7% of it is lost. The
fluid has to be replaced before 40% has been lost, or the equipment it is being used in will be damaged. How
many purifications can the fluid be put through before it must be replaced?
a) 13
c) 19
b) 14
d) 23
____ 26. Which of the following is NOT true of the graph of
?
y
6
5
4
3
2
1
1
–1
2
3
4
5
6
7
8
9
10
x
–2
–3
–4
a)
b)
c)
d)
The graph has a vertical asymptote.
As the value of x increases, the slope of the tangent line will become less steep.
As x grows larger, the changes in the slope of the tangent line become smaller.
The tangent lines at very small values of x have negative slopes.
Short Answer
27. If ( x , y ) is on the graph of
graph of
, state the coordinates (in terms of x and y) that would be on the
.
28. Given that (10, 1) is on the graph of the parent function
, what transformations need to be
performed on the graph so that it is the product of a function that images (10, 1) to (23, 5).
29. The parent function
is vertically stretched by 3, reflected in the y-axis, horizontally translated 4
units to the left and vertically translated 2.5 units up. What is the equation of the vertical asymptote of the
transformed function?
30. Simplify
31. Write
32. Evaluate
.
as a single logarithm.
.
33. Solve
for x.
34. Solve
for x. Round your answer to two decimal places.
35. A bacteria culture doubles every 20 minutes. How many hours will it take a culture of 60 bacteria to grow to
a population of 8400?
36. A shade allows light to pass through from a lamp, but reduces the intensity of the light. The intensity of the
light is reduced by 15% if the fabric is 1 mm thick. Each additional millimetre of fabric reduces the intensity
by another 15%. Produce an equation that models the relationship between the thickness of the fabric (t) and
the intensity of the light (i).
37. Solve
.
38. Solve
39. Solve
.
.
40. The population of a town is increasing at a rate of 6.2% per year. The city council believes they will have to
add another elementary school when the population reaches 100 000. If there are currently 76 000 people
living in the town, how long do they have before the new school will be needed?
Unit 8 Application and Thinking Review
Answer Section
MULTIPLE CHOICE
1. ANS:
OBJ:
2. ANS:
OBJ:
3. ANS:
OBJ:
4. ANS:
OBJ:
5. ANS:
6. ANS:
OBJ:
7. ANS:
8. ANS:
9. ANS:
10. ANS:
11. ANS:
12. ANS:
13. ANS:
OBJ:
14. ANS:
15. ANS:
16. ANS:
17. ANS:
OBJ:
18. ANS:
OBJ:
19. ANS:
OBJ:
20. ANS:
OBJ:
21. ANS:
OBJ:
22. ANS:
OBJ:
23. ANS:
OBJ:
24. ANS:
OBJ:
25. ANS:
OBJ:
A
PTS: 1
REF: Thinking
8.2 - Transformations of Logarithmic Functions
A
PTS: 1
REF: Application
8.2 - Transformations of Logarithmic Functions
B
PTS: 1
REF: Application
8.2 - Transformations of Logarithmic Functions
C
PTS: 1
REF: Communication
8.2 - Transformations of Logarithmic Functions
D
PTS: 1
REF: Application OBJ: 8.3 - Evaluating Logarithms
B
PTS: 1
REF: Communication
8.3 - Evaluating Logarithms
A
PTS: 1
REF: Thinking
OBJ: 8.3 - Evaluating Logarithms
B
PTS: 1
REF: Thinking
OBJ: 8.4 - Laws of Logarithms
D
PTS: 1
REF: Application OBJ: 8.4 - Laws of Logarithms
B
PTS: 1
REF: Application OBJ: 8.4 - Laws of Logarithms
A
PTS: 1
REF: Thinking
OBJ: 8.4 - Laws of Logarithms
B
PTS: 1
REF: Thinking
OBJ: 8.5 - Solving Exponential Equations
D
PTS: 1
REF: Communication
8.5 - Solving Exponential Equations
B
PTS: 1
REF: Application OBJ: 8.5 - Solving Exponential Equations
C
PTS: 1
REF: Application OBJ: 8.5 - Solving Exponential Equations
A
PTS: 1
REF: Thinking
OBJ: 8.5 - Solving Exponential Equations
D
PTS: 1
REF: Communication
8.6 - Solving Logarithmic Equations
B
PTS: 1
REF: Application
8.6 - Solving Logarithmic Equations
A
PTS: 1
REF: Thinking
8.6 - Solving Logarithmic Equations
C
PTS: 1
REF: Application
8.6 - Solving Logarithmic Equations
C
PTS: 1
REF: Application
8.7 - Solving Problems with Exponential and Logarithmic Functions
A
PTS: 1
REF: Thinking
8.7 - Solving Problems with Exponential and Logarithmic Functions
C
PTS: 1
REF: Application
8.7 - Solving Problems with Exponential and Logarithmic Functions
A
PTS: 1
REF: Application
8.7 - Solving Problems with Exponential and Logarithmic Functions
A
PTS: 1
REF: Thinking
8.7 - Solving Problems with Exponential and Logarithmic Functions
26. ANS: D
PTS: 1
REF: Thinking
OBJ: 8.8 - Rates of Change in Exponential and Logarithmic Functions
SHORT ANSWER
27. ANS:
( x 4 , 2y
3)
PTS: 1
REF: Thinking
OBJ: 8.2 - Transformations of Logarithmic Functions
28. ANS:
One possible answer: Horizontal stretch by 2, Vertical stretch by 5, Horizontal translation 3 units to the right
PTS: 1
29. ANS:
x=
REF: Application
OBJ: 8.2 - Transformations of Logarithmic Functions
PTS: 1
30. ANS:
164
REF: Thinking
OBJ: 8.2 - Transformations of Logarithmic Functions
PTS: 1
31. ANS:
REF: Thinking
OBJ: 8.3 - Evaluating Logarithms
PTS: 1
32. ANS:
0
REF: Thinking
OBJ: 8.4 - Laws of Logarithms
PTS: 1
33. ANS:
270
REF: Thinking
OBJ: 8.4 - Laws of Logarithms
PTS: 1
34. ANS:
0.53
REF: Application
OBJ: 8.4 - Laws of Logarithms
PTS: 1
35. ANS:
2.4 hours
REF: Thinking
OBJ: 8.5 - Solving Exponential Equations
PTS: 1
36. ANS:
REF: Application
OBJ: 8.5 - Solving Exponential Equations
PTS: 1
37. ANS:
4
REF: Application
OBJ: 8.5 - Solving Exponential Equations
REF: Thinking
OBJ: 8.6 - Solving Logarithmic Equations
PTS: 1
38. ANS:
7
PTS: 1
39. ANS:
8
REF: Thinking
OBJ: 8.6 - Solving Logarithmic Equations
PTS: 1
40. ANS:
4.6 years
REF: Thinking
OBJ: 8.6 - Solving Logarithmic Equations
PTS: 1
REF: Application
OBJ: 8.7 - Solving Problems with Exponential and Logarithmic Functions