Name: ________________________ Period: ___________________ Date: __________
ID: A
PreCalc 12 Chapter 5 Review Pack v1
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Consider the exponential function y  a x , a  0 . Which of these statements is false?
A.
B.
C.
D.
____
2. The graph of y  9 x is translated 5 units left and 4 units up. Identify the equation of the image graph.
A.
B.
____
y  4  (9)
y  4  9x  5
y0
y1
y  4(9) 5 x
D. y  5  9 x  4
C.
C.
D.
y  k
yk
4. Write 64 4 as a power of 4.
A. 4
B. 4
____
(x  5)
3. Determine the equation of the horizontal asymptote of the graph of y  k  c(a)
A.
B.
____
The graph has y-intercept 1.
The graph does not have an x-intercept.
The function has a horizontal asymptote with equation y  a .
The range of the function is y  0 .
3
2
7
2
C. 4 6
D. 4
5
2
5. Solve: 7 x  49 x  4
A. x = 4
B. x = –2
C. x = –4
D. x = 8
1
d(x  h)
, a  0, c  0, d  0 .
Name: ________________________
____
6. Solve: 27 x  5  9 x  3
1
21
B. x = 21
1
21
D. x = –21
C. x = 
A. x =
____
____
7. Solve: 343 x 
2
A. x =
9
7
B. x =
9
3
49
C. x =
2
3
D. x = 2
8. Given log b a  c , which statement is true?
A. a  b c
B. c  a b
____
ID: A
C. c  b a
D. a  c b
9. Which of these expressions is NOT equal to log160 ?
A. log80  log2
B. log48  log 112
C. log16  log10
D. log8  log 20
____ 10. Write as a single logarithm: 4log 3 4  log 3 12  3
A. log 3 4
64000
B. log 3
3
C. log 3 576
D. log 3 7
____ 11. Which logarithm has the least value?
A. log 3 479
B. log 2 943
C. log 5 371
D. log 4 265
2
Name: ________________________
ID: A
____ 12. The graph of y  log 3 x is stretched vertically by a factor of 6, and then translated 8 units down. Identify the
equation of the image graph.
A.
B.
y  8  6log 3 (x)
y  log 3 ÊÁË 6(x  8) ˆ˜¯
C.
y  6  8 log 3 (x)
D.
y  8  6 log 3 (x)
____ 13. To repay a loan, Chloe makes payments quarterly for 10 years.
How many payments does she make?
A. 14
B. 40
C. 4
D. 10
____ 14. The graphs of y  log 3 x and its transformation image y  g(x) are shown.
Identify the transformations.
A. A translation of 3 units right and 2 units down
1
B. A vertical compression by a factor of
4
C. A vertical stretch by a factor of 4
1
D. A horizontal compression by a factor of
4
3
Name: ________________________
ID: A
____ 15. The Richter scale measures the intensity of an earthquake. The magnitude, M, of an earthquake can be
ÊÁ I ˆ˜
determined using the function M  log ÁÁÁÁ ˜˜˜˜ , where I microns is the intensity of the earthquake, and S microns
ËS ¯
is the intensity of a standard earthquake.
In June 2011, New Zealand experienced an earthquake with magnitude 6.0.
Calculate the intensity of the earthquake in New Zealand in terms of a standard earthquake.
A. 10 60 S
B. 10 6 S
C. 6S
D. 60S
____ 16. The Richter scale measures the intensity of an earthquake. The magnitude, M, of an earthquake can be
ÊÁ I ˆ˜
determined using the function M  log ÁÁÁÁ ˜˜˜˜ , where I microns is the intensity of the earthquake, and S microns
ËS ¯
is the intensity of a standard earthquake.
In September 2011, Vancouver Island experienced an earthquake with magnitude 6.4.
In June 2001, Peru experienced an earthquake with magnitude 8.4.
How many times as intense as the Vancouver Island earthquake was the Peru earthquake?
A. 10 2 times as intense
B. 3 times as intense
C. 10 3 times as intense
D. Approximately 1.3 times as intense
____ 17. The decibel scale measures the intensity of sound. The loudness of a sound, L decibels (dB), can be
ÊÁ I ˆ˜
determined using the function L  10log ÁÁÁÁ ˜˜˜˜ , where I is the intensity of the sound and I 0 is the intensity of
ÁË I 0 ˜¯
the quietest sound that can be detected.
The loudness of a vacuum cleaner is 75 dB and the loudness of a snowmobile is 115 dB.
How many times as intense as the sound of a vacuum cleaner is the sound of a snowmobile?
A. 40 times as intense
B. 10 40 times as intense
C. 10 4 times as intense
D. Approximately 1.5 times as intense
4
Name: ________________________
ID: A
____ 18. The pH scale measures the acidity or alkalinity of a solution. A solution that has a pH of 7 is neutral. For each
increase of 1 pH, a solution is 10 times as alkaline. For each decrease of 1 pH, a solution is 10 times as acidic.
A sample of juice has a pH of 2.6. A sample of milk has a pH of 6.5.
To the nearest whole number, how many times as acidic as the milk is the juice?
A. 1976 times as acidic
B. 3 times as acidic
C. 25 times as acidic
D. 7943 times as acidic
____ 19. The future value formula is used when an amount, FV dollars, is saved through a series of equal investments
at equal time intervals, and the compounding period of the interest is equal to the time interval for the
R[(1  i) n  1]
investments. The formula is: FV 
, where R dollars is the regular investment, i is the interest
i
rate per compounding period, and n is the number of investments.
A student wants to buy a trumpet in 15 months for $1900. The student plans to make 15 equal monthly
deposits into a savings account that pays 4% annual interest, compounded monthly.
How much should the student deposit each month?
A. $2.09
B. $123.74
C. $94.89
D. $8.58
Short Answer
20. Could this table of values describe an exponential function?
x
y
–2
1
4
0
–1
0
1
4
1
1
2
9
4
21. For the exponential function y  k  ca
d(x  h)
, a  0, c  0, d  0 , determine the y-intercept of its graph.
5
Name: ________________________
ID: A
22. The graph of y  2 x is shown below.
Sketch the graph of y  2(2) 0.25x on the same grid.
ÊÁ 1 ˆ˜ x
23. The graph of y  ÁÁÁÁ ˜˜˜˜ is shown below.
Ë3¯
ÊÁ 1 ˆ˜ x  1
Sketch the graph of y  2 ÁÁÁÁ ˜˜˜˜
on the same grid.
Ë3¯
6
Name: ________________________
ID: A
ÁÊ 1 ˜ˆ˜
˜˜
24. Evaluate: log 8 ÁÁÁÁ
˜
Ë 128 ¯
Ê
ˆ
25. Evaluate: log 4 ÁÁÁ 256 4 ˜˜˜
Ë
¯
26. To the nearest tenth, estimate the value of log 2 34 .
27. Write as a single logarithm:
4
log x  3 log 3 y  6log 3 z
5 3
28. Write as a single logarithm: 4  log 2 x
ÁÊÁ n ˜ˆ˜
29. Given logn 
Ö 1.447 , determine the approximate value of log ÁÁÁ 1000 ˜˜˜ .
Ë
¯
Ê
ˆ
30. Solve: 203  7 ÁÁ 6 x  4 ˜˜
Ë
¯
Give the solution to the nearest hundredth.
31. Solve: 3 x  9  5 x  6
Give the solution to the nearest hundredth.
32. Solve: log 2 (x  3 )  log 2 (x  6 )  1  log 2 (x  2 )  log 2 (x  4 )
Problem
33. A principal of $900 is invested at 3% annual interest, compounded bi-weekly (every 2 weeks).
To the nearest year, when will the amount be $1300?
7
Name: ________________________
ID: A
34. Given log3 
Ö 0.4771 and log5 
Ö 0.6990 , determine the approximate value of log(10 125) without using a
calculator.
35. Write as a single logarithm: log(4x 2  13x  35)  log(x 2  25)
36. a)
b)
i)
ii)
iii)
iv)
v)
x
Use transformations to sketch the graph of the exponential function y  3 (2)  2 .
Determine:
whether the function is increasing or decreasing
the intercepts
the equation of the asymptote
the domain of the function
the range of the function
37. Use algebra to determine the x-intercept of the graph of y  k  c log a d(x  h), a  0, c  0, d  0 .
È ˘
È ˘
38. The pH of a solution can be described by the equation pH  log ÍÍÍÍ H + ˙˙˙˙ , where ÍÍÍÍ H + ˙˙˙˙ is the hydrogen-ion
Î ˚
Î ˚
concentration in moles/litre.
a) The hydrogen-ion concentration in a sample of watermelon is 3.2  10 6 moles/litre.
Determine the pH of the watermelon, to the nearest tenth.
b) A sample of lemon juice has a pH of 2.6.
Determine the hydrogen-ion concentration of the lemon juice, to four decimal places.
39. Two students each graduate with a student loan of $17 000 at 4.4% annual interest. Both students make
payments totalling $4212 per year. Student A makes payments of $351 per month, and the interest is
compounded every month. Student B makes payments of $162 every two weeks, and the interest is
compounded every two weeks. Compare the lengths of times it takes each student to repay the loan. Is one
payment plan significantly better than the other? Explain.
8