MHF4U1- ASSIGNMENT 7A
True/False
Indicate whether the statement is true or false.
____ 1. For any values a > 0 and b > 0, it can be shown that .
____ 2.
____ 3.
____ 4.
____ 5.
____ 6.
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 7. Express as a power with a base of 2.
a. / / c. /b. / / d. /
____ 8. Express as a power with a base of 2.
a. / / c. /b. / / d. /
____ 9. Express as a power with a base of 4.
a. / / c. /b. / / d. /
____ 10. Solve the equation .
a. / / c. /b. / / d. /
____ 11. Solve the equation .
a. / / c. /b. / / d. /
____ 12. Solve the equation .
a. / / c. /b. / / d. /
____ 13. Solve the equation .
a. / / c. /b. / / d. /
____ 14. Solve the equation .
a. / / c. /b. / / d. /
____ 15. A 25-g sample of a substance decays to 13 g in 14 years. The half-life of this substance is approximately
a. / 3.77 years / c. / 8.59 yearsb. / 14.8 years / d. / 14.1 years
____ 16. The half-life of a radioactive substance is 97 years. If 10 mg are produced after a reaction, approximately how long will it take for only 1 mg to remain?
a. / 29 years / c. / 322 yearsb. / 180 years / d. / 462 years
____ 17. The value, D, in dollars, of a certain vehicle as a function of time, t, in years, depreciates according to the function . How long will it take for this vehicle to be worth $20 000?
a. / 0.80 years / c. / 4.26 yearsb. / 1.75 years / d. / 3.23 years
____ 18. Evaluate, using the laws of logarithms.
a. / 2 / c. / 6b. / 4 / d. / 8
____ 19. Evaluate, using the laws of logarithms.
a. / 1 / c. / 4b. / 2 / d. / 8
____ 20. Evaluate, using the laws of logarithms.
a. / 2 / c. / 6b. / 4 / d. / 8
____ 21. Evaluate, using the laws of logarithms.
a. / 3 / c. / 5b. / 4 / d. / 6
____ 22. Write as a single logarithm.
a. / / c. /b. / / d. /
____ 23. Write as a single logarithm.
a. / / c. /b. / / d. /
____ 24. The restrictions on the variable in the expression is
a. / x > 3 / c. / x < –3b. / x < 3 / d. / A and C
____ 25. The restriction on the variable in the expression is
a. / x > 4 / c. / x <b. / x > 3 / d. / A and C
Completion
Complete each statement.
26. Some algebraic methods of solving exponential equations lead to ______that are not valid solutions to the original equation.
27. The graph of is a ______of the graph .
28. The ______of logarithms state that
29. The quotient law of logarithms state that ______.
Short Answer
30. Solve the equation .
31. The half-life of strontium-90 is 29 years. Find the mass remaining after 18 years if a 100-g sample is left to decay.
32. A car depreciates at a rate of 20% per year. How long will it take for the car to reach half its original value?
33. Solve the equation . Leave your answer in exact form.
34. Evaluate, using the laws of logarithms.
35. Simplify. State any restrictions on the variable.
36. Write as the sum or difference of logarithms. Simplify, if possible.
Problem
37. A 200-g sample of a radioctive substance is placed in a chamber to be tested. After 3 h, 140 g of the sample remains.
a) Determine the half-life of this substance.
b) Graph the amount of the substance remaining as a function of time.
38. A chemist has a 20-mg sample of polonium-218. He needs exactly 81.5% of it for an experiment. Given that the half-life of polonium-218 is approximately 3.1 min, how many seconds will it take for the sample to decay to the desired mass?
39. Rewrite the equation in quadratic form and solve. Check your solution.
40. Evaluate, using the laws of logarithms.
41. Graph the function on a grid.
a) Graph the functions on the same grid.
b) Explain the effect of the constant k in the function .
MHF4U1- ASSIGNMENT 7A
Answer Section
TRUE/FALSE
1. ANS: T PTS: 1 DIF: 2 REF: Knowledge and Understanding
OBJ: Section 7.1 LOC: A1.4, A3.1 TOP: Exponential and Logarithmic Functions
KEY: equivalent forms, change the base, logarithm
2. ANS: F PTS: 1 DIF: 1 REF: Knowledge and Understanding
OBJ: Section 7.3 LOC: A1.4 TOP: Exponential and Logarithmic Functions
KEY: product law of logarithms
3. ANS: F PTS: 1 DIF: 1 REF: Knowledge and Understanding
OBJ: Section 7.3 LOC: A1.4 TOP: Exponential and Logarithmic Functions
KEY: quotient law of logarithms
4. ANS: T PTS: 1 DIF: 1 REF: Knowledge and Understanding
OBJ: Section 7.3 LOC: A1.4 TOP: Exponential and Logarithmic Functions
KEY: quotient law of logarithms
5. ANS: F PTS: 1 DIF: 1 REF: Knowledge and Understanding
OBJ: Section 7.3 LOC: A1.4 TOP: Exponential and Logarithmic Functions
KEY: product law of logarithms, quotient law of logarithms
6. ANS: F PTS: 1 DIF: 1 REF: Knowledge and Understanding
OBJ: Section 7.3 LOC: A1.4 TOP: Exponential and Logarithmic Functions
KEY: power law of logarithms
MULTIPLE CHOICE
7. ANS: C PTS: 1 DIF: 1 REF: Knowledge and Understanding
OBJ: Section 7.1 LOC: A1.4 TOP: Exponential and Logarithmic Functions
KEY: equivalent forms, change the base
8. ANS: D PTS: 1 DIF: 1 REF: Knowledge and Understanding
OBJ: Section 7.1 LOC: A1.4 TOP: Exponential and Logarithmic Functions
KEY: equivalent forms, change the base, power law of logarithms
9. ANS: B PTS: 1 DIF: 2 REF: Knowledge and Understanding
OBJ: Section 7.1 LOC: A1.4 TOP: Exponential and Logarithmic Functions
KEY: equivalent forms, change the base
10. ANS: C PTS: 1 DIF: 1 REF: Knowledge and Understanding
OBJ: Section 7.1 LOC: A3.2, A1.4 TOP: Exponential and Logarithmic Functions
KEY: exponential equation, change the base
11. ANS: B PTS: 1 DIF: 2 REF: Knowledge and Understanding
OBJ: Section 7.1 LOC: A3.2, A1.4 TOP: Exponential and Logarithmic Functions
KEY: exponential equation, change the base
12. ANS: C PTS: 1 DIF: 1 REF: Knowledge and Understanding
OBJ: Section 7.2 LOC: A3.2, A1.4 TOP: Exponential and Logarithmic Functions
KEY: exponential equation, different bases
13. ANS: C PTS: 1 DIF: 1 REF: Knowledge and Understanding
OBJ: Section 7.2 LOC: A3.2, A1.4 TOP: Exponential and Logarithmic Functions
KEY: exponential equation, different bases
14. ANS: D PTS: 1 DIF: 2 REF: Knowledge and Understanding
OBJ: Section 7.2 LOC: A3.2, A1.4 TOP: Exponential and Logarithmic Functions
KEY: exponential equation, different
15. ANS: B PTS: 1 DIF: 3
REF: Knowledge and Understanding; Application OBJ: Section 7.2
LOC: A3.4, A2.4 TOP: Exponential and Logarithmic Functions
KEY: exponential equation, half-life
16. ANS: C PTS: 1 DIF: 3
REF: Knowledge and Understanding; Application OBJ: Section 7.2
LOC: A3.4, A2.4 TOP: Exponential and Logarithmic Functions
KEY: exponential equation, half-life
17. ANS: D PTS: 1 DIF: 2
REF: Knowledge and Understanding; Application OBJ: Section 7.2
LOC: A3.4, A2.4 TOP: Exponential and Logarithmic Functions
KEY: exponential equation, exponential decay
18. ANS: C PTS: 1 DIF: 1 REF: Knowledge and Understanding
OBJ: Section 7.3 LOC: A1.4 TOP: Exponential and Logarithmic Functions
KEY: laws of logarithms
19. ANS: A PTS: 1 DIF: 1 REF: Knowledge and Understanding
OBJ: Section 7.3 LOC: A1.4 TOP: Exponential and Logarithmic Functions
KEY: laws of logarithms
20. ANS: B PTS: 1 DIF: 2 REF: Knowledge and Understanding
OBJ: Section 7.3 LOC: A1.4 TOP: Exponential and Logarithmic Functions
KEY: laws of logarithms
21. ANS: C PTS: 1 DIF: 2 REF: Knowledge and Understanding
OBJ: Section 7.3 LOC: A1.4 TOP: Exponential and Logarithmic Functions
KEY: laws of logarithms
22. ANS: A PTS: 1 DIF: 2 REF: Knowledge and Understanding
OBJ: Section 7.3 LOC: A1.4 TOP: Exponential and Logarithmic Functions
KEY: laws of logarithms
23. ANS: D PTS: 1 DIF: 2 REF: Knowledge and Understanding
OBJ: Section 7.3 LOC: A1.4 TOP: Exponential and Logarithmic Functions
KEY: laws of logarithms
24. ANS: D PTS: 1 DIF: 3 REF: Knowledge and Understanding
OBJ: Section 7.3 LOC: A1.4 TOP: Exponential and Logarithmic Functions
KEY: laws of logarithms, restriction
25. ANS: D PTS: 1 DIF: 3 REF: Knowledge and Understanding
OBJ: Section 7.3 LOC: A1.4 TOP: Exponential and Logarithmic Functions
KEY: laws of logarithms, restriction
COMPLETION
26. ANS: extraneous roots
PTS: 1 DIF: 1 REF: Knowledge and Understanding
OBJ: Section 7.2 LOC: A3.2, A3.4 TOP: Exponential and Logarithmic Functions
KEY: exponential equation, extraneous root
27. ANS: vertical translation
PTS: 1 DIF: 2 REF: Knowledge and Understanding
OBJ: Section 7.3 LOC: A2.4, A3.1 TOP: Exponential and Logarithmic Functions
KEY: transformation, equivalent forms
28. ANS: product law
PTS: 1 DIF: 1 REF: Knowledge and Understanding
OBJ: Section 7.3 LOC: A1.4, A3.1 TOP: Exponential and Logarithmic Functions
KEY: product law of logarithms
29. ANS:
PTS: 1 DIF: 1 REF: Knowledge and Understanding
OBJ: Section 7.3 LOC: A1.4, A3.1 TOP: Exponential and Logarithmic Functions
KEY: quotient law of logarithms
SHORT ANSWER
30. ANS:
PTS: 1 DIF: 3 REF: Knowledge and Understanding
OBJ: Section 7.1 LOC: A1.4, A3.2 TOP: Exponential and Logarithmic Functions
KEY: equivalent forms, exponential equation, changing the base
31. ANS:
65.0 g
PTS: 1 DIF: 2 REF: Knowledge and Understanding; Application
OBJ: Section 7.2 LOC: A3.2, A3.4 TOP: Exponential and Logarithmic Functions
KEY: exponential equation, half-life
32. ANS:
3.1 years
PTS: 1 DIF: 3 REF: Knowledge and Understanding; Application
OBJ: Section 7.2 LOC: A3.2, A3.4 TOP: Exponential and Logarithmic Functions
KEY: exponential equation, depreciation
33. ANS:
PTS: 1 DIF: 3 REF: Knowledge and Understanding
OBJ: Section 7.2 LOC: A1.4, A3.2 TOP: Exponential and Logarithmic Functions
KEY: exponential equation, different bases
34. ANS:
3
PTS: 1 DIF: 2 REF: Knowledge and Understanding
OBJ: Section 7.3 LOC: A1.4, A3.1 TOP: Exponential and Logarithmic Functions
KEY: laws of logarithms
35. ANS:
PTS: 1 DIF: 4 REF: Knowledge and Understanding
OBJ: Section 7.3 LOC: A3.1, A1.4 TOP: Exponential and Logarithmic Functions
KEY: laws of logarithms, restriction
36. ANS:
PTS: 1 DIF: 2 REF: Knowledge and Understanding
OBJ: Section 7.3 LOC: A1.4, A3.1 TOP: Exponential and Logarithmic Functions
KEY: laws of logarithms
PROBLEM
37. ANS:
a) 5.83 years
b)
PTS: 1 DIF: 3 REF: Knowledge and Understanding; Application
OBJ: Section 7.2 LOC: A2.4, A3.2, A3.4
TOP: Exponential and Logarithmic Functions KEY: exponential equation, half-life
38. ANS:
approximately 54.9 s
PTS: 1 DIF: 3 REF: Knowledge and Understanding; Thinking; Application
OBJ: Section 7.2 LOC: A3.2, A3.4 TOP: Exponential and Logarithmic Functions
KEY: exponential equation, half-life
39. ANS:
x = 0 and
PTS: 1 DIF: 2 REF: Knowledge and Understanding
OBJ: Section 7.2 LOC: A3.1, A3.2 TOP: Exponential and Logarithmic Functions
KEY: exponential equation
40. ANS:
PTS: 1 DIF: 4 REF: Knowledge and Understanding
OBJ: Section 7.3 LOC: A1.4, A3.1, A3.3
TOP: Exponential and Logarithmic Functions KEY: laws of logarithms
41. ANS:
a)
b) vertical translation up by
PTS: 1 DIF: 3 REF: Knowledge and Understanding; Thinking; Communication
OBJ: Section 7.3 LOC: A1.4, A2.4, D3.3
TOP: Exponential and Logarithmic Functions, Characteristics of Functions
KEY: logarithm, transformation