Unit 8 Exam

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1. Divide

2.Use the properties of logarithms to evaluate log7343.

4

3

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3. After taking 3 quizzes, your average is 79 out of 100. What must your average score be on the next five quizzes to increase your average to 84?

87

81

86

85

4. It is not necessary to check all solutions of the derived equation in the original equation to find whether any of them are not solutions of the original equation.

True

False

5.

Find the equation of the graph.

y = 1.5 • 2 x

y = 1.5 • 0.5 x

y = 2 • 1.5 x

y = 1.5 x

6.Write 5 log x – 4 log ( x – 4) as a single logarithm.

log x 5( x – 4)4

none of these

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7. Evaluate e 4.

10.8731

54.5982

55.8322

0.0183

8.Write an exponential function to model this situation: a population of 260 animals increases at an annual rate of 9%.

f ( x ) = 260(0.109) x

f ( x ) = 260(0.91) x

f ( x ) = 260(1.09) x

f ( x ) = 260(0.091) x

9. Multiply

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10.Write the function that models this relationship:

11. Solve the question below.

399

400

506

505

12. Simplify

z + 4

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13. Find the inverse of the relation. Graph the given relation and its inverse.

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14. Find

15. You decide to buy a boat that costs $4200. The normal depreciation for such a boat is 14% per year. If you pay for the boat with a 4-year loan, how much will the boat be worth after you have paid off the loan?

$4,144.00

$1,902.57

$2,893.63

$2,297.43

16. A continuously compounded account starts with $1500 in principal. The annual interest rate is 9.1%. What is the balance after 30 years?

$11,083.58

$25,190.45

$22,999.33

$20,456.62

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17.Given log 5 = P and log 2 = Q , find log 10.

P – Q

P + Q

PQ

18. Let f ( x ) = 3 x + 7 and g ( x ) = 4 x – 2. Find ( f g ) (–6).

-47

-72

-71

-46

19. Expand

20. For an annual rate of change of –31%, find the corresponding growth or decay factor.

1.69

0.69

1.31

0.31

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21.Write 5 log x + 4 log ( x – 2) as a single logarithm.

log x 5( x – 2)4

log x ( x – 2)

20 log x ( x – 2)

none of these

22. A group of college students is volunteering for Help the Homeless during their spring break. They are putting the finishing touches on a house they built. Working alone, Katalin can paint a certain room in 3 hours. Lena can paint the same room in 8 hours. Identify the equation that can be used to find how long it will take them working together to paint the room. How many hours will it take them to paint the room?

3 + 8 = x ; 2.3 h

23. Suppose that x and y vary inversely. Write a function rule for the function that x = 9 when y = 4.

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24. Solve the question below.

25.Write an exponential function to model this situation: a population of 420 animals decreases at an annual rate of 21%. Then predict the value of the function after 5 years (to the nearest whole number).

f ( x ) = 420(0.79) x ; 129 animals

f ( x ) = 420(1.21) x ; 1089 animals

f ( x ) = 420(1.21) x ; 2541 animals

f ( x ) = 420(0.79) x ; 1659 animals

26.Use the properties of logarithms to evaluate

14

21

1

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27. Identify the graph of y = 2 x 2 – 5 and its inverse.

28. A complex fraction is a fraction that has a fraction in either its numerator or denominator, or in both its numerator and denominator.

True

False

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29.What is the quotient when

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30. Identify the graph of f ( x ) = 3 x .

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31. Find the inverse of f ( x ) = 3 x 2. Is the inverse a function?

32. Find the annual percent increase or decrease that y = 0.35(2.3) x models.

–80.5%

+130%

+230%

–65%

33. Is the relationship between the values in the table a direct variation, an inverse variation, or neither? Write an equation to model either variation.

direct variation; y = 2.5 x

direct variation; y = 2.5 x + 7.5

neither

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34. Multiply

x ; x ≠ –6, –3, 0

none of these

35. Simplify

36. Let f ( x ) = 4 – x 2 and g ( x ) = 2 – x . Find f ( x ) • g ( x ).

– x 3 + 2 x 2 – 4 x + 8

– x 2 – x + 6

2 + x

x 3 – 2 x 2 – 4 x + 8

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37.Graph

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38.

Simplify

588

39. A continuously compounded account starts with $2500 in principal. The annual interest rate is 11.3%. What is the balance after 15 years?

$13,616.61

$12,455.68

$18,472.64

$15,245.60

40.Write an exponential function to model this situation: a population of 300 animals increases at an annual rate of 13%.

f ( x ) = 300(0.087) x

f ( x ) = 300(0.113) x

f ( x ) = 300(0.87) x

f ( x ) = 300(1.13) x

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41. Identify the graph of y = 2 x + 7 and its inverse.

42.Use the properties of logarithms to evaluate log4256.

4

5

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43. The Bangor Coat Factory found that the number of coats sold N varies directly as their advertising budget A and inversely as the price of each coat P . The Bangor Coat Factory sold 10,800 coats when $30,000 was spent on advertising and the price of a coat was set at $50. Determine the number of coats sold when the amount spent on advertising is increased to $70,000.

25,200 coats

1400 coats

24,480 coats

3888 coats

44.

Solve

x = 4

no solution

45.Given log 15 = B and log 3 = C , find log 5.

B – C

B + C

BC

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46.Graph y = 4 x – 3 as a translation of its parent function.

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47. Solve the question below.

48. Let f ( x ) = 3 x 2 + 10 x – 8 and g ( x ) = x + 4.

–9 x + 6, all real numbers x ≠ -4

9 x – 6, all real numbers x ≠ -4

3 x + 2, all real numbers x ≠ -4

3 x – 2, all real numbers x ≠ -4

49. Solve the question below.

9

7

14

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50. For the function f ( x ) = (4 – 2 x )2, find f –1 and the domain and range of f and f –1. Determine whether f –1 is a function.

51. Simplify

2x

5x

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