Free Printable Alg2 Test 14 Review

1.

What is the equation of the horizontal asymptote of the function

y = 2(0.3)^{x - 1} - 4?

a)

y = -4

b)

y = 2

c)

y = 0.3

d)

y = 4

2.

Which function does not model exponential decay?

a)

y = 3/4 e^-3x

b)

y = 4/3 e ^-3x

c)

y = 4 e^-3x

d)

y = 4 e^3x

3.

Which expression is equivalent to x?

a)

$\log x$

b)

$\log2^x$

c)

$\log10^x$

d)

$\log100^x$

4.

Which of the following is an equivalent expression for $2\log_43+\log_42?$

a)

$2\log_46$

b)

$\log_46$

c)

$\log_412$

d)

$\log_418$

5.

Which of the following is not equivalent to $\log_58?$

a)

$\log_5\left(\frac{16}{2}\right)$

b)

$2\log_54$

c)

$3\log_52$

d)

$\log_54+\log_52$

6.

What is the range of this exponential function?
$y=-3\cdot5^{\left(x+3\right)\ }$

a)

$\left(-\infty,\ 0\right)$

b)

all real numbers

c)

$\left(-\infty,3\right)$

d)

$\left(0,\infty\right)$

7.

A town doubles its size every 33 years. If the population is currently 6,000, what will the population be in 66 years?

a)

12,000

b)

24,000

c)

198,000

d)

396,000

8.

Condense into single logarithm.

18log₉a + 6log₉b

a)

log₉a¹⁸b⁶

b)

log_a18 + log_b6 = 9

c)

log₉(a¹⁸+ b⁶)

d)

log_b9(a¹⁸ + log₆)

9.

Expand.

log₄a⁶b⁵

a)

6log₄a - 5log₄b

b)

log₄a + log₄b = 30

c)

4log₆a + 4log₅b

d)

6log₄a + 5log₄b

10.

True or False?

log_xx^x = x

a)

True

b)

False

11.

Evaluate.

\log_3\ \frac{1}{243}

a)

5

b)

-5

c)

3

d)

-3

12.

Evaluate.

log₃1

a)

-1

b)

1

c)

3

d)

0

13.

Use multiple log properties to write as a single log:
3log₂x - log₂y + log₂z

a)

log₂(x/(yz))

b)

log₂(x³yz)

c)

log₂(x³z/y)

d)

log₂(x³/(yz))

14.

Find the domain and range of:
f(x) = log₂(x)

a)

D: all real numbers
R: y > 0

b)

Domain: all real numbers
Range: all real numbers

c)

Domain: x > 0
Range: all real numbers

d)

Domain: all real numbers
Range: y < 0

15.

Identify the asymptote of the function $f\left(x\right)=\log_5\ \left(x-1\right)$ .

a)

x = 5

b)

x = -1

c)

y = 0

d)

x = 1

16.

What is the equation of the asymptote of the function $y=\log_5\left(x+3\right)+5$ ?

a)

x = -3

b)

x = 5

c)

y = -3

d)

y = 5

17.

What is the range of the function $f\left(x\right)=\log_2\left(x-4\right)-3$ ?

a)

$y>-3$

b)

$x>0$

c)

$\left(-\infty,\ \infty\right)$

d)

$y>0$

18.

The asymptote of y = log₂x + 9 will shift...

a)

right 9 to x = 9

b)

left 9 to x = -9

c)

not shift at all and remain x = 0

19.

The equation for this exponential function is

a)

y = 1(2^x)

b)

y = 1(4^x)

c)

y = 3x

d)

y = 1(3^x)

20.

The growth factor for this table is

a)

2

b)

4

c)

12

d)

144

21.

The equation for this table is

a)

y = 1(2^x)

b)

y = 1(12^x)

c)

y = 12x

d)

y = 12x + 1

22.

The y-intercept for this table is

a)

800

b)

200

c)

100

d)

2

23.

The number of mosquitoes at the beginning of the summer was 4,000. The population of mosquitoes is expected to grow at a rate of 25% a month. How many mosquitoes will there be after 4 months?

a)

9766

b)

9006

c)

9765

d)

5433

24.

What does the model P=A(1+r)^t best represent?

a)

Exponential growth

b)

Simple Interest

c)

Compound Interest

d)

Exponential Decay

25.

The attendance at the art museum at the New Year’s opening was 250 people. The attendance has been increasing at a rate of 3% each month. How many people will attend by the end of a year?

a)

356

b)

265

c)

5825

d)

1329

26.

Classify the model as Exponential GROWTH or DECAY.
A=10(1.01)³

a)

Growth

b)

Decay

27.

Classify the model as Exponential GROWTH or DECAY.
A=1200(.85)⁶

a)

Growth

b)

Decay

28.

A 78 gram sample of Uranium loses half of its mass each year. How much is left after 6 years?

a)

13 grams

b)

6.5 grams

c)

1.22 grams

d)

592.31 grams

29.

James' 70 in. giant peach doubles in size every week. Write an expression that would represent how big the peach is after 5 weeks.

a)

70(2)³⁵

b)

70(2)⁵

c)

2(70)⁵

d)

5(70)²

30.

The value of a painting is $12,000 in 1990 and increases by 8% of its value each year. Write and evaluate an expression to estimate the paintings value in 2005.

a)

1.08(12,000)^t = $36,000

b)

12,000(1.08)^t = $38, 066

c)

12,000(0.5)^t = $10,000

d)

12,000(0.92)^t= $40,000

31.

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

a)

y=5000(0.7)^x

b)

y=30(5000)^x

c)

y=5000(1.3)^x

d)

y=5000x^x

32.

A population of fish starts at 8,000 and decreases by 6% per year. What is the population of fish after 10 years?

a)

14327

b)

4309

c)

839

d)

7680

33.

Use y = e^x to evaluate e^1.7 to 4 decimal places.

a)

5.4739

b)

4.6211

c)

2.7183

d)

4.8929

34.

Kennedy won $3,000 from a radio contest. If she puts this money in a bank account that earns 2.9% interest compounded quarterly, how much total will she earn in 10 years?

a)

$4915.59

b)

$3933.28

c)

$2979.81

d)

$4005.09

35.

Caiden earned $475 from mowing lawns last summer. He deposited this money in an account that pays an interest rate of 3.8% compounded annually. What will be his balance after 15 year?

a)

$827.52

b)

$831.10

c)

$839.45

d)

$846.80

36.

Riley invested $1,000 in savings bonds. If the bonds earn 6.75% interest compounded semi-annually, how much total will Riley earn in 15 years?

a)

$1,584.62

b)

$2,651.39

c)

$2,706.86

d)

$1,825.10

37.

Caiden earned $475 from mowing lawns last summer. He deposited this money in an account that pays an interest rate of 3.8% compounded monthly. What will be his balance after 15 years?

a)

$827.52

b)

$839.17

c)

$839.45

d)

$846.80

38.

Determine the balance in the account if you deposited $4,000 at an interest rate of 3.4% compounded quarterly for three years.

a)

$4422.03

b)

$4427.62

c)

$4428.90

d)

$4429.51

39.

If $1,000 is invested at 16% interest, compounded continuously, for five years, what is the ending balance?

a)

$1,225,54

b)

$2,225.54

c)

$22,255.40

d)

$225.54

40.

You invest $1600 at an annual interest rate of 4.6% compounded continuously. How much will you have in the account after 4 years.

a)

$800.26

b)

$6,701.28

c)

$10,138.07

d)

$1,923.23

41.

Simply the expression. $e^{-4}\cdot e^6$

a)

$e^{-2}$

b)

$\frac{1}{e^2}$

c)

$e^2$

d)

$e^{24}$

e)

$e^{-24}$

42.

Simplify the expression. $\frac{11e^9}{22e^{10}}$

a)

$\frac{2}{e}$

b)

$\frac{1}{2e}$

c)

$\frac{e^{-1}}{2}$

d)

$2e$

43.

Simplify: $\left(4e^{-2x}\right)^3$

a)

$\frac{4}{e^{6x}}$

b)

$\frac{1}{64e^{6x}}$

c)

$64e^{6x}$

d)

$\frac{64}{e^{6x}}$

44.

1.) Simplify
(2a²b⁴z)(6a³b²z⁵)

a)

8a⁵b⁶z⁶

b)

12a⁶b⁸z⁵

c)

12a⁵b⁶z⁶

d)

8a⁶b⁸z⁵

45.

Solve

a)

p⁴

b)

p^-4

c)

1/p^-4

d)

1/p⁴

46.

Make this negative exponent positive.
9^-3

a)

9³

b)

1/9^-3

c)

1/9³

d)

729

47.

a)

4y⁶

b)

4y²²

c)

30y⁶

d)

30y²²

48.

a)

1¹⁰

b)

1²⁶

c)

z¹⁰

d)

z²⁶

49.

Simplify the expression:

$5x^9\cdot-6x^2$

a)

$-30x^{11}$

b)

$-30x^{18}$

c)

$-x^{11}$

d)

$-x^{18}$

50.

Simplify the expression:

$\frac{12x^9y^4z^2}{24x^3y^4z^6}$

a)

$2x^3z^3$

b)

$\frac{x^6}{2z^4}$

c)

$\frac{x^3}{2z^3}$

d)

$\frac{2x^6}{x^4}$

51.

Simplify: $\log_73+\log_76$

a)

$\log_79$

b)

$\log_7\left(\frac{1}{2}\right)$

c)

$\log_7729$

d)

undefined

52.

Simplify: $\log_4\left(x+4\right)-\log_4\left(x-5\right)$

a)

$\log_49$

b)

$\log_4\left(2x-1\right)$

c)

$\log_4\left(x^2-x-20\right)$

d)

$\log_4\left(\frac{x+4}{x-5}\right)$

53.

Simplify: $2\log_3\left(11x\right)$

a)

$\log_3\left(22x\right)$

b)

$\log_3\left(121x\right)$

c)

$\log_3\left(121x^2\right)$

d)

$\log_3\left(11x^2\right)$

54.

Simplify: $\frac{1}{4}\log_516+3\log_5x$

a)

$\log_5\left(4x^3\right)$

b)

$\log_5\left(2x^3\right)$

c)

$\log_5\left(6x\right)$

d)

$\log_5\left(\frac{2}{x^3}\right)$

55.

Simplify: $2\log_2x-\log_2\left(x+3\right)$

a)

$\log_2\left(x^3+3x^2\right)$

b)

$\log_2\left(2x^2+6x\right)$

c)

$\log_2\left(\frac{x^2}{x+3}\right)$

d)

$\log_2\left(\frac{2x}{x+3}\right)$

56.

Simplify: $\frac{1}{4}\log_281+\frac{1}{2}\log_249$

a)

$\log_221$

b)

$\log_210$

c)

$\log_2\left(\frac{3}{7}\right)$

d)

$\log_244.75$

57.

Simplify: $\frac{1}{2}\log_964+\log_9x$

a)

$\log_9\left(32x\right)$

b)

$\log_9\left(\frac{32}{x}\right)$

c)

$\log_9\left(\frac{8}{x}\right)$

d)

undefined

58.

A log with a base of 10 is known as the (a) log.

59.

Expand this logarithm.

a)

b)

c)

d)

60.

Expand this logarithm.

a)

b)

c)

d)

61.

Expand this logarithm.

a)

b)

c)

d)

62.

Solve for x: 3^{2x – 6} = 81

a)

x = log 4

b)

x = 5

c)

x = 4

d)

x = -1

63.

Graph: f(x) = 2^-x+2 - 1

a)

A

b)

B

c)

C

d)

D

64.

Determine the equation of the asymptote?

a)

x=3

b)

x=4

c)

y=-4

d)

y=4

65.

Expand the logarithm
log₁₀ 7x

a)

(log₁₀ 7)(log₁₀ x)

b)

log₁₀ 7 + log₁₀ x

c)

7log₁₀ x

d)

xlog₁₀ 7

66.

In March, 2020, before the Covid-19 lockdown, 1,200,000 Texans had applied for unemployment. During the COVID-19 lockdown, the number of people applying for unemployment increased by 4% each month. What exponential function can be used to find the number of people applying for unemployment after x months of COVID-19 lockdown? (a)

Choose from the below words

$y=1,200,000\left(1.04\right)^x$

$y=\ 1,200,000\left(0.04\right)^x$

$y=1,200,000\left(1.4\right)^x$

$y=1,200,000\left(0.06\right)^x$

67.

Which of the following exponential functions represents an initial value of 1450 and a decay of 18% for x years?

a)

$y=1450\left(0.18\right)^x$

b)

$y=1450\left(1.18\right)^x$

c)

$y\ =\ 1450\ -\left(0.18\right)^x$

d)

$y=1450\left(0.82\right)^x$

68.

A flea medicine breaks down at a rate of 20% per hour. This is the rate of decay of the medicine. The initial dose is 60 milligrams. Which of the following represent the equation the models the amount of flea medicine left in an animal?

a)

$y=60\left(.2\right)^x$

b)

$y=20\left(60\right)^x$

c)

$y=60\left(.8\right)^x$

d)

$y=60\left(1.2\right)^x$

69.

This is an example of:

(a)

Choose from the below words

Exponential Growth

Linear Growth

Linear Decay

Exponential Decay

70.

Which number is the BASE?
2³= 8

a)

2

b)

3

c)

8

d)

not here

71.

What is the value of 100⁰?

a)

1

b)

0

c)

100

72.

Simplify the expression:
c⁴⋅c³=

a)

^c12

b)

c⁴⁺³

c)

c⁷

73.

According to exponent rules, when we raise a power to another exponent we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

74.

(g⁵)⁸

a)

g¹³

b)

5g⁸

c)

g⁴⁰

d)

8g⁵

75.

What is the asymptote of y = 2^x - 3

a)

y = 0

b)

y = -3

c)

x = 0

d)

x = -3

76.

As x → ∞ , f(x) →

a)

-4

b)

-3

c)

∞

d)

-∞

77.

Which equation matches the graph?

a)

y = 4^x + 3

b)

y = 4^x - 3

c)

y = 4^{(x + 3)}

d)

y = 4^{(x - 3)}

78.

What is the domain of the function?

a)

x > -4

b)

y > -5

c)

y < -4

d)

all real numbers

79.

Find the domain.

a)

x < 1

b)

ℝ

c)

x > 0

d)

x < 0

80.

Compare f(x) = 3^x- 4 with the basic function g(x) = 3^x

a)

4 units up

b)

4 units to the left

c)

4 units to the right

d)

4 units down

81.

What kind of transformation is represented?

a)

up 1 unit

b)

left 1 unit

c)

right 1 unit

d)

down 1 unit

82.

What does the n stand for in this formula?

a)

Initial amount

b)

Final amount

c)

Rate

d)

Time

e)

The number of times compounded per year

83.

Olivia would like to buy some new furniture for her home. She decides to buy the furniture on credit with 9.5% interest compounded quarterly. If she spent $7,400, how much total will she have paid after 8 years.

a)

$15,415.94

b)

$15,683.28

c)

$15,927.56

d)

$16,109.05

84.

You invest $1600 at an annual interest rate of 4.6% compounded continuously. How much will you have in the account after 4 years.

a)

$800.26

b)

$6,701.28

c)

$10,138.07

d)

$1,923.23

85.

Simply the expression. $e^{-4}\cdot e^6$

a)

$e^{-2}$

b)

$\frac{1}{e^2}$

c)

$e^2$

d)

$e^{24}$

e)

$e^{-24}$

86.

Simplify the expression. $\frac{11e^9}{22e^{10}}$

a)

$\frac{2}{e}$

b)

$\frac{1}{2e}$

c)

$\frac{e^{-1}}{2}$

d)

$2e$

87.

Simplify: $\left(4e^{-2x}\right)^3$

a)

$\frac{4}{e^{6x}}$

b)

$\frac{1}{64e^{6x}}$

c)

$64e^{6x}$

d)

$\frac{64}{e^{6x}}$

88.

Rewrite log_b(xⁿ)

a)

nlog_bx

b)

(log_bx)ⁿ

c)

xⁿlog_bx

d)

log_b(xⁿ)

89.

Write log_b(x/y) as two logs

a)

log_bx-log_by

b)

log_bx+log_by

c)

log_bx*log_by

d)

log_bx/log_by

90.

Write log_b(xy) as two logs

a)

log_bx+log_by

b)

log_bx-log_by

c)

log_bx*log_by

d)

log_bx/log_by

91.

Use the change of base rule to rewrite this problem:

log₇729

a)

log(7)/log(729)

b)

log(729)/log(7)

92.

Use the change of base rule to rewrite this problem:

log₅75

a)

log(75)/log(5)

b)

log(5)/log(75)

93.

Put the steps in the correct order to solve the equation.

$5^{\left(3x-1\right)}\cdot5^{\left(2x-5\right)}=5^{\left(x+6\right)}$

a)

$\left(3x-1\right)+\left(2x-5\right)=x+6$

b)

$5x-6=x+6$

c)

$4x-6=6$

d)

$4x=12$

e)

$x=3$

1)

2)

3)

4)

5)

94.

Put the steps in the correct order to solve the equation.

$64^x=8^{\left(3x+1\right)}$

a)

$\left(8^2\right)^x=8^{\left(3x+1\right)}$

b)

$2x=3x+1$

c)

$-x=1$

d)

$x=-1$

1)

2)

3)

4)

95.

Put the steps in the correct order to solve the equation.

$\frac{1}{216}=36^{\left(3x+6\right)}$

a)

$\frac{1}{6^3}=\left(6^2\right)^{\left(3x+6\right)}$

b)

$6^{-3}=\left(6^2\right)^{\left(3x+6\right)}$

c)

$-3=6x+12$

d)

$-15=6x$

e)

$-\frac{5}{2}=x$

1)

2)

3)

4)

5)

96.

Put the steps in the correct order to solve the equation.

$32^{\left(x+6\right)}\cdot\frac{1}{2}=8^{\left(x-1\right)}$

a)

$\left(2^5\right)^{\left(x+6\right)}\cdot2^{\left(-1\right)}=\left(2^3\right)^{\left(x-1\right)}$

b)

$5x+30+-1=3x-3$

c)

$5x+29=3x-3$

d)

$2x=-32$

e)

$x=-16$

1)

2)

3)

4)

5)

97.

Put the steps in the correct order to solve the equation.

$16\cdot2^{\left(6m\right)}=2^{\left(3m-8\right)}$

a)

$2^{\left(4\right)}\cdot2^{\left(6m\right)}=2^{\left(3m-8\right)}$

b)

$4+6m=3m-8$

c)

$3m=-12$

d)

$m=-4$

1)

2)

3)

4)

98.

Put the steps in the correct order to solve the equation.

$256^{\left(y\right)}\cdot16^{\left(y-1\right)}=4^{\left(2y-22\right)}$

a)

$\left(4^4\right)^{\left(y\right)}\cdot\left(4^2\right)^{\left(y-1\right)}=4^{\left(2y-22\right)}$

b)

$4y+2y-2=2y-22$

c)

$6y-2=2y-22$

d)

$4y=-20$

e)

$y=-5$

1)

2)

3)

4)

5)

99.

Put the steps in the correct order to solve the equation.

$36^{\left(n-3\right)}\cdot216^{\left(n\right)}=216^{\left(2n+1\right)}$

a)

$\left(6^2\right)^{\left(n-3\right)}\cdot\left(6^3\right)^{\left(n\right)}=\left(6^3\right)^{\left(2n+1\right)}$

b)

$2n-6+3n=6n+3$

c)

$5n-6=6n+3$

d)

$-9=n$

1)

2)

3)

4)

100.

$2^{\left(3x-1\right)}\cdot4^{\left(5x-7\right)}=8^{\left(x+4\right)}$

101.

Condense into a single logarithm.

$\log_515+3\cdot\log_53$

a)

$\log_5405$

b)

$\log_{40}5$

c)

$\log_{ }\frac{\text{}x^5}{\text{}y^3}$

d)

$\log_3x^{11}$

102.

Condense into a single logarithm.

$\log_7272-\frac{1}{2}\cdot\log_764$

a)

$\log_{34}7$

b)

$\log_734$

c)

$\log_{ }\frac{\text{}3^5}{\text{}\left(y-2\right)^3}$

d)

$\log_3x^{11}$

103.

Evaluate. Use the change of base formula if necessary. Write answer as x = _

$\log_5\frac{\text{1}}{\text{25}}$

104.

Expand the logarithm.

$\log_4\left(3z^2\right)^4$

a)

$4\log_4\left(3\right)+8\log_4\left(z\right)$

b)

$12+\log_4\left(6z\right)$

c)

$1+2\log_4\left(12z\right)$

105.

Expand the logarithm.

$\log_{10}\left(\frac{\text{x}^5}{\text{y}^3}\right)^2$

a)

$10\log_{10}\left(x\right)-6\log_{10}\left(y\right)$

b)

$5\log_5\left(x\right)+3\log_2\left(y\right)$

c)

$4\log_{ }\left(x^5\right)-3\log_{ }\left(y^3\right)$

d)

$\log_xy+\log_yx$

106.

Write the expression in exponential form.

$\log_464=3$

107.

Write the expression in exponential form.

$\log_y9=\frac{1}{5}$

108.

Select the correct expression in logarithmic form.

$3^{-3}=\frac{1}{27}$

a)

$\log_3\ \frac{1}{27}=-3$

b)

$\log_{-3}27=1$

c)

$\log_3\frac{-1}{27}=3$

d)

l $\log_{27}-3=1$

109.

Select the correct expression in logarithmic form.

$7^x=12$

a)

$\log_712=x$

b)

$\log_{-7}x=12$

c)

$\log_7\frac{-x}{12}=0$

d)

$\log_{12}7=x$

110.

Common Logarithm - A (a) with (b) (c) is called a common logarithm and can be written (d) the base.

(e) -----> $\log_{ }x$

Choose from the below words

logarithm

base

10

without

$\log_{10}x$

111.

Use the change of base formula to evaluate the logarithm.

(Round your answer to four decimal places)

$\log_635$

112.

Use the change of base formula to evaluate the logarithm.

(Round your answer to four decimal places)

$\log_786$

113.

Solve $\log_2\left(x+8\right)=\log_264$

a)

x=16

b)

x=24

c)

x=56

d)

x=40

114.

Solve $\log_8\left(3x+7\right)=\log_8\left(7x+4\right)$

a)

$x=\frac{3}{4}$

b)

$x=3$

c)

$x=6$

d)

$x=\frac{4}{3}$

115.

Solve $\log_6x+\log_69=\log_654$

a)

x=6

b)

x=45

c)

x=7

d)

x=36

116.

Solve

$\log_7n=\frac{2}{3}\log_78$

a)

n=1

b)

n=3

c)

n=6

d)

n=4

117.

Solve $\log_9\left(3u+14\right)-\log_95=\log_92u$

a)

u=4

b)

u=6

c)

u=2

d)

u=1

Alg2 Test 14 Review - Exponents and Logs

Total questions: 117

Worksheet time: 3hrs 3mins

Similar Resources on Wayground