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ID: A
Algebra II: Chapter 8 Study Guide
Short Answer
Graph the exponential function.
1. y = 4 x
2. y = 3 (1.9)
x
3. An initial population of 505 quail increases at an annual rate of 23%. Write an exponential function to model
the quail population.
4. Write an exponential function y = ab x for a graph that includes (1, 15) and (0, 6).
Graph the function. Identify the horizontal asymptote.
5. y = 5 (2.1)
x
ÊÁ 1 ˆ˜ x
˜˜ .
˜
7
Ë ˜¯
6. Graph y = − 5 ÁÁÁ
Á
7. Graph y = 7 (6)
x+2
+ 1.
8. The half-life of a certain radioactive material is 85 days. An initial amount of the material has a mass of 801
kg. Write an exponential function that models the decay of this material. Find how much radioactive material
remains after 10 days. Round your answer to the nearest thousandth.
9. Use a graphing calculator. Use the graph of y = e x to evaluate e 1.7 to four decimal places.
10. Suppose you invest $1600 at an annual interest rate of 4.6% compounded continuously. How much will you
have in the account after 4 years?
11. The table shows some notable earthquakes that occurred in recent years. How many times more energy was
released by the earthquake in Peru than by the earthquake in Mexico?
Earthquake Location
Date
Italy
October 31, 2002
El Salvador
February 13, 2001
Afghanistan
May 30, 1998
Mexico
January 22, 2003
Arequipa, Peru
June 23, 2001
[Source: World Almanac 2004, p. 190]
Write the equation in logarithmic form.
12. 6 4 = 1, 296
1
Richter Scale Measure
5.9
6.6
6.9
7.6
8.1
Name: ________________________
ID: A
Evaluate the logarithm.
13. log 5
1
625
14. log 3 243
The pH of a liquid is a measure of how acidic or basic it is. The concentration of hydrogen ions in a
ÍÈ ˙˘
liquid is labeled ÍÍÍ H + ˙˙˙ . Use the formula pH = −log [H + ] to answer questions about pH.
Î ˚
−3
15. Find the pH level, to the nearest tenth, of a liquid with [H +] about 6.5 × 10 .
16. The pH of a juice drink is 2.6. Find the concentration of hydrogen ions in the drink.
Graph the logarithmic equation.
17. y = log5 x
18. y = log(x + 1) − 7
Write the expression as a single logarithm.
19. 5 log b q + 2 log b y
20. log 3 4 − log 3 2
Expand the logarithmic expression.
21. log 7
n
2
22. log 3 11p 3
23. log b
57
74
24. A company with loud machinery needs to cut its sound intensity to 37% of its original level. By how many
decibels would the loudness be reduced? Use the formula L = 10 log
I
. Round to the nearest hundredth.
Io
25. Solve 15 2x = 36. Round to the nearest ten-thousandth.
26. Use the Change of Base Formula to evaluate log 4 20. Then convert log 4 20 to a logarithm in base 3. Round to
the nearest thousandth.
27. Use a graphing calculator. Solve 5 4x = 2115 by graphing. Round to the nearest hundredth.
28. Solve log(4x + 10) = 3.
29. Solve log 3x + log 9 = 0. Round to the nearest hundredth if necessary.
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Name: ________________________
ID: A
Write the expression as a single natural logarithm.
30. 3 ln 3 + 3 lnc
31. The sales of lawn mowers t years after a particular model is introduced is given by the function y =
5500 ln(9t + 4), where y is the number of mowers sold. How many mowers will be sold 2 years after a model
is introduced? Round the answer to the nearest whole number.
32. The generation time G for a particular bacteria is the time it takes for the population to double. The bacteria
increase in population is shown by the formula G =
t
, where t is the time period of the population
3.3 log a P
increase, a is the number of bacteria at the beginning of the time period, and P is the number of bacteria at
the end of the time period. If the generation time for the bacteria is 6 hours, how long will it take 8 of these
bacteria to multiply into a colony of 7681 bacteria? Round to the nearest hour.
33. Solve ln(2x − 1) = 8. Round to the nearest thousandth.
Use natural logarithms to solve the equation. Round to the nearest thousandth.
34. 6e 4x − 2 = 3
35. The amount of money in an account with continuously compounded interest is given by the formula
A = Pe rt , where P is the principal, r is the annual interest rate, and t is the time in years. Calculate to the
nearest hundredth of a year how long it takes for an amount of money to double if interest is compounded
continuously at 6.2%. Round to the nearest tenth.
x
ÁÊ 2 ˆ˜˜
˜˜ represents exponential growth or exponential
Ë 3 ˜¯
36. Without graphing, determine whether the function y = 7 ÁÁÁ
Á
decay.
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Name: ________________________
ID: A
37. The exponential decay graph shows the expected depreciation for a new boat, selling for $ 3500, over 10
years.
a. Write an exponential function for the graph.
b. Use the function in part a to find the value of the boat after 9.5 years.
Essay
38. Suppose you invest $580 at 10% compounded continuously.
a. Write an exponential function to model the amount in your investment account.
b. Explain what each value in the function model represents.
c. In how many years will the total reach $3600? Show your work.
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ID: A
Algebra II: Chapter 8 Study Guide
Answer Section
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8-1.1 Exponential Growth
8-1.1 Exponential Growth
8-1.1 Exponential Growth
8-1.1 Exponential Growth
8-1.2 Exponential Decay
8-2.1 Comparing Graphs
8-2.1 Comparing Graphs
8-2.1 Comparing Graphs
8-2.2 The Number e
8-2.2 The Number e
8-3.1 Writing and Evaluating Logarithmic Expressions
8-3.1 Writing and Evaluating Logarithmic Expressions
8-3.1 Writing and Evaluating Logarithmic Expressions
8-3.1 Writing and Evaluating Logarithmic Expressions
8-3.1 Writing and Evaluating Logarithmic Expressions
8-3.1 Writing and Evaluating Logarithmic Expressions
8-3.2 Graphing Logarithmic Functions
8-3.2 Graphing Logarithmic Functions
8-4.1 Using the Properties of Logarithms
8-4.1 Using the Properties of Logarithms
8-4.1 Using the Properties of Logarithms
8-4.1 Using the Properties of Logarithms
8-4.1 Using the Properties of Logarithms
8-4.1 Using the Properties of Logarithms
8-5.1 Solving Exponential Equations
8-5.1 Solving Exponential Equations
8-5.1 Solving Exponential Equations
8-5.2 Solving Logarithmic Equations
8-5.2 Solving Logarithmic Equations
8-6.1 Natural Logarithms
8-6.1 Natural Logarithms
8-5.1 Solving Logarithmic Equations
8-6.2 Natural Logarithmic and Exponential Equations
8-6.2 Natural Logarithmic and Exponential Equations
8-6.2 Natural Logarithmic and Exponential Equations
8-1.2 Exponential Decay
8-1.2 Exponential Decay
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ESSAY
38. OBJ: 8-6.2 Natural Logarithmic and Exponential Equations
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