Name: ________________________ Class: ___________________ Date: __________
ID: A
Review Exponential & Logarithmic Functons Multiple Choice Identify the choice that best completes the statement or answers the question. ____
1. Use x = −3 , –2, 0, 1, 2 to graph the function f (x ) = 2 x . Then graph its inverse. Describe the domain and range of the inverse function. c. a.
ÔÏ Ô¸ The domain of f −1 (x ) is ÌÔ x |x > 0 ˝Ô , and Ó ˛ the range is all real numbers. b.
¸Ô ˝Ô . ˛
The domain of f −1 (x ) is all real ÏÔ numbers, and the range is ÌÔ y || y < 0 Ó
¸Ô ˝Ô . ˛
d.
The domain of f −1 (x ) is all real ÏÔ numbers, and the range is ÌÔ y || y ≥ 0 Ó ____
The domain of f −1 (x ) is all real ÔÏ numbers, and the range is ÌÔ y || y > 0 Ó
¸Ô ˝Ô . ˛
2. A initial investment of $10,000 grows at 11% per year. What function represents the value of the investment after t years? a. f(t) = 10000(0.11) t c. f(t) = 10000(1.11)t b.
f(t) = 10000(12) t
d.
1
f(t) = 10000(1.11) t
Name: ________________________
____
3. Evaluate log 4
1 16
ID: A
.
a.
1 4
c.
–2
b.
4
d.
2
____
4. A wildlife biologist in Nova Scotia is testing the pH of stream water. She hopes that the pH of the water is greater than 5.5 so that Atlantic Salmon returning this year to their natal streams will be able to reproduce. The hydrogen ion concentration of the water is 0.0000019 moles per liter. To the nearest tenth, what is the ÍÈ ˙˘ pH of the water? (Recall that pH = −log ÍÍÍ H + ˙˙˙ .) Î ˚ a. 1.9 × 10 −6 c. 6.0 b. 5.7 d. –6.0
____
5. Simplify the expression log 5 125 4 . a. 3 b. 25
c. d.
12 625
6. Simplify the expression log 4 64 . a. 16 b. 64
c. d.
4 3
____
____
____
____
7. Evaluate log 9 243 . If necessary, round your answer to the nearest tenth. a. 3 c. 27 b. 2.5 d. 1.4
Ê 100 ˆ P 8. The altitude of an aircraft, h, in miles, is given by h = − ÁÁÁ 9 ˜˜˜ log B , where P = the outside air pressure, and B Ë ¯ = the atmospheric pressure at sea level. Let B = 31 inches of mercury (in. Hg). What is the outside air pressure at a height of 3.6 miles? Round your answer to the nearest tenth. a. 14.7 in. Hg c. 1.2 in. Hg b. 65.4 in. Hg d. –0.5 in. Hg 9. Simplify log 7 x 3 − log 7 x . a.
log 7 (x 3 − x)
c.
log 7 2x
b.
2log 7 x
d.
2(x 3 − x)
____ 10. Re-write the logarithm using the properites of logs: log 3 27 −3 a. log 3 − 9 c. 27log 3 3 b.
−3log 3 27
____ 11. Express log 5 20 + log 5 6 as a single logarithm. a. log 5 26 b.
6log 5 20
d.
log 3 3 3
c.
log 5 120
d.
log 5 20 6
2
Name: ________________________
ID: A
____ 12. Write the logarithmic equation log 9 81 = 2 in exponential from. a. b.
9 81 = 2 9 2 = 81
c. d.
2 −9 = 81 2 9 = 81
____ 13. Mira bought $300 of Freerange Wireless stock in January of 1998. The value of the stock is expected to increase by 7.5% per year. Use a graph to predict the year the value of Mira’s stock will reach $700. a. 1999 c. 2009 b. 2004 d. 2014 Matching Match each vocabulary term with its definition. a. exponential decay b. exponential equation c. exponential function d. exponential growth e. exponential regression f. exponential expression g. exponential relation ____ 14. a function of the form f(x) = ab x , where a and b are real numbers with a ≠ 0, b > 0, and b ≠ 1 ____ 15. an exponential function of the form f(x) = ab x in which 0 < b < 1 ____ 16. an exponential function of the form f(x) = ab x in which b > 1 Match each vocabulary term with its definition. a. exponent b. base c. inverse function d. parent function e. common logarithm f. natural logarithm g. asymptote h. inverse relation ____ 17. a line that a graph gets closer to as the value of a variable becomes extremely large or small ____ 18. a logarithm whose base is 10, denoted log 10 or just log ____ 19. the value of b in a function of the form f(x) = ab x , where a and b are real numbers with a ≠ 0, b > 0, and b ≠ 1. ____ 20. a logarithmic function is the __________ _________ of an exponential function
3
Name: ________________________
ID: A
Short Answer 21. A bacteria population starts at 2,032 and decreases at about 15% per day. Write a function representing the number of bacteria present each day. After how many days will there be fewer than 321 bacteria?
22. Write the exponential equation 2 3 = 8 in logarithmic form.
23. Write the logarithmic equation log 4 16 = 2 in exponential from.
24. Express log 3 6 + log 3 4.5 as a single logarithm.
25. Express log 2 64 − log 2 4 as a single logarithm.
26. Re-write log 6 216 5 using the properties of logarithms.
x
27. Tell whether the function y = 2 (5) shows growth or decay. Then graph the function.
4
ID: A
Review Exponential & Logarithmic Functons Answer Section MULTIPLE CHOICE 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.
ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS:
A D C B C D B A B B C B C
NAT: 12.5.1.e
NAT: 12.5.1.e
MATCHING 14. ANS: C 15. ANS: A 16. ANS: D 17. 18. 19. 20.
ANS: ANS: ANS: ANS:
G E B C
1
ID: A
SHORT ANSWER 21. ANS: f(x) = 2032(0.85) t
After about 11.3 days, there will be fewer than 321 bacteria. NAT: 12.5.1.e 22. ANS: log2 8 = 3 23. ANS: 4 2 = 16 24. ANS: 3 25. ANS: 4 26. ANS: 5log 6 216
2
ID: A 27. ANS: This is an exponential growth function.
NAT: 12.5.1.h
3