Free Printable Alg Chapter 7 Review - Exponentials and logs

1.

What is the domain and range of the function y=2^x?
Use the graph to help!

a)

Domain: −∞<x<∞
Range: y>0

b)

Domain: −∞<x<∞
Range: y>1

c)

Domain: −2<x<∞
Range: y>0

d)

Domain: −∞<x<∞
Range: y>0

2.

Which function is exponential?

a)

f(x)

b)

h(x)

c)

g(x)

3.

Is the pictured graph growth, decay, or linear or none?

a)

Exponential Growth

b)

Exponential Decay

c)

Linear

d)

None

4.

What type of function is y = 7(5/4)^x?

a)

Exponential Growth

b)

Exponential Decay

c)

Linear

d)

None of the above

5.

What function is present?

a)

Absolute Value

b)

Exponential Decay

c)

Linear Equation

d)

Exponential Growth

6.

What type of function is present? f(x) = 2^x?

a)

Exponential Growth

b)

Linear Equation

c)

Absolute Value

d)

Exponential Decay

7.

Solve: 9^8-x = 27^x-3

a)

x = 5

b)

x = -5

c)

x = 1/5

d)

x = -1/5

8.

Solve: 2^x = 4^x+1

a)

x = -2

b)

x = 2

c)

x = -3

d)

x = 3

9.

Sovle for x:
5^{-3x - 1} = 25

a)

x = -1

b)

x = -4

c)

x = -3

d)

x = 1

10.

Solve for p:
4^p+2 = 64

a)

p = -16/9

b)

p = 1

c)

p = 8

d)

p = 7/6

11.

2^-m = 2^3m-3

a)

4/3

b)

3/4

c)

2

d)

1

12.

8^3x+3 = 8⁶

a)

x=28

b)

x=3

c)

x=1

d)

x=12

13.

Solve for a:
5^{a + 2} = 1/125

a)

-1

b)

-6/7

c)

-5

d)

4

14.

Solve

a)

-1/3

b)

-3

c)

-1

d)

3

15.

Rewrite as an exponential: $\log_93=\frac{1}{2}$

a)

$9^{\frac{1}{2}}=3$

b)

$3^{\frac{1}{2}}=9$

c)

$9^3=\frac{1}{2}$

d)

$\left(\frac{1}{2}\right)^9=3$

16.

Rewrite as an exponential: $\log_7\left(\frac{1}{49}\right)=-2$

a)

$7^{\frac{1}{49}}=-2$

b)

$\left(\frac{1}{49}\right)^{-2}=7$

c)

$7^{-2}=\frac{1}{49}$

d)

$\left(-2\right)^7=\frac{1}{49}$

17.

Rewrite as a log: y = 7^x

a)

log₇(x) = y

b)

log_y(7) = x

c)

log_x(y) = 7

d)

log₇(y) = x

18.

Rewrite as a log: x = 11^y

a)

log₁₁(y) = x

b)

log_y(11) = x

c)

log₁₁(x) = y

d)

log_x(y) = 11

19.

Rewrite as a log: 7⁰ = 1

a)

log₇(1) = 0

b)

log₀(7) = 1

c)

log₇(0) = 1

d)

log₁(0) = 7

20.

What is the base for the following log:

y = log (x)

a)

1

b)

0

c)

10

d)

2

21.

Find x: log₂(32) = x

a)

x = 5

b)

x = 16

c)

x = 4

d)

x = 6

22.

Find x: log₅(x) = 4

a)

x = 20

b)

x = 25

c)

x = 625

d)

x = 125

23.

Find x: log_x(25) = 2

a)

x = 1

b)

x = 12.5

c)

No Solution

d)

x = 5

24.

Find x: $\log_7\left(\frac{1}{7}\right)=x$

a)

x = -1

b)

x = 1

c)

x = 0

d)

No Solution

25.

Find x: log₅(x) = 0

a)

No Solution

b)

x = 0

c)

x = 5

d)

x = 1

26.

Rewrite the equation in logarithmic form.

a)

b)

c)

d)

27.

Rewrite the equation in logarithmic form.

a)

b)

c)

d)

28.

Rewrite the equation in logarithmic form.

a)

b)

c)

d)

29.

Solve

log₂(x + 5) = 3

a)

3

b)

4

c)

5

d)

6

30.

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

31.

Change 6.75% to a decimal.

a)

67.5

b)

.675

c)

675

d)

.0675

32.

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

a)

$827.52

b)

$831.10

c)

$839.45

d)

$846.80

33.

The Arnold's took out a loan for $195,000 to purchase a home. At a 4.3% interest rate, how much total will they have paid after 30 years?

a)

$412,749.79

b)

$529.305.61

c)

$689,546.99

d)

$640,891.53

34.

The Henley's took out a loan for $195,000 to purchase a home. At a 4.3% interest rate how much interest will they have paid after 30 years?

a)

$690,000

b)

$429,305.61

c)

$689,546.99

d)

$494,546.99

35.

Hannah invested $4000. How much money will she have in 15 years if the interest rate of 6% is being compounded continuously?

a)

9839.42

b)

32412.71

c)

9838.41

d)

32412.72

36.

Solve the following for 'x';

log₆(3x - 2) = log₆(5x - 8)

a)

x = 3

b)

x = 2

c)

x = -1

d)

No Solution

37.

Evaluate log₄1

a)

¹/₄

b)

0

c)

-1

d)

not possible

38.

e^ln(f)

a)

f

b)

e

c)

e^f

d)

undefined

39.

The best interpretation of the value $1.08$ in the function $f\left(x\right)=36492\left(1.08\right)^x$ is the (a) factor. It also represents an 8% (b) , each year, in the area occupied by the toads

Choose from the below words

growth

increase

decay

decrease

40.

The function represented by this graph is $f\left(x\right)=20\left(2\right)^x$ . How many customers would there be by the 9th week?

41.

Given the exponential function $y=3\left(\frac{1}{2}\right)^x$ , what is the value of y when $x=-3$ ?

a)

$24$

b)

$\frac{1}{2}$

c)

$\frac{3}{8}$

d)

$-\frac{9}{2}$

42.

What is the horizontal asymptote for the graph of

f(x)=13(0.5)^x?

a)

y=0.5

b)

y=13

c)

y=6

d)

y=0

43.

For $f\left(x\right)=3^x$ , find the correct graph, asymptote, domain and range.

a)

b)

44.

Write the exponential equation for this situation.

Mr. Exponent told his English class that each week students tend to forget one sixth of the vocabulary words they learned the previous week. If the students learn 30 words, write an exponential equation to describe the number of words forgotten after x weeks.

a)

$A=30\left(6\right)^x$

b)

$A=30\left(\frac{1}{6}\right)^x$

c)

$A=\frac{1}{6}\left(30\right)^x$

d)

$A=\frac{1}{6}\left(\frac{1}{30}\right)^x$

45.

log₆(2x + 3) = 3

a)

x = 106.5

b)

x = 100

c)

x = 16

d)

x = 50

46.

a)

Line n

b)

Line j

c)

Line k

d)

Line m

47.

Jiminy Cricket is in the yard when it starts to rain. As more rain falls, Jiminy can't jump as far. This can be modeled by $3\left(\frac{1}{2}\right)^t$ . How far away from the house was Jiminy when the rain began?

a)

.75

b)

1/2

c)

3

d)

1.5

48.

Rapunzel's hair grew 16% each week she was in the tower. If her hair was 20 inches long when she was placed in the tower, what is a model for the growth of Rapunzel's hair?

a)

$16\left(1+.20\right)^w$

b)

$16\left(1+20\right)^w$

c)

$20\left(1+.16\right)^w$

d)

$20\left(1+16\right)^w$

49.

If Jack's Bean stalk grew 75% every hour and the bean stalk was 2 foot when he started watching it grow, what is a model for the growth of the bean stalk?

a)

$2\left(1+75\right)^h$

b)

$2\left(1+.75\right)^h$

c)

$75\left(1+2\right)^h$

d)

$7\left(1+.02\right)^h$

50.

If the wolf blew down 36% of the little pig's house each time he puffed and blew, and the house started at 35 feet high, what is a model for how high the house is with each huff and puff?

a)

$36\left(1-35\right)^p$

b)

$36\left(1-.35\right)^p$

c)

$35\left(1-36\right)^p$

d)

$35\left(1-.36\right)^p$

51.

Which is the same as $300\left(1-.17\right)^t$

a)

$300\left(1.17\right)^t$

b)

$300\left(.83\right)^t$

c)

$300\left(.93\right)^t$

52.

INLINE CHOICE EXAMPLE 2

An online retailer adjusts the price of an item each month that the item goes unsold. The price of the unsold item, in dollars, after x months can be modeled by the exponential function $f\left(x\right)=90\left(0.85\right)^x$ .

Choose the correct answer from each drop-down menu to complete the sentences.

The initial price of the item before price adjustments is (a) .

The price of the item (b) at a rate of (c) each month.

Choose from the below words

$90

decreases

15%

$15

85%

90%

$85

increases

53.

A certain type of bacteria doubles in number every hour. If you start with 3 bacteria, the number of bacteria after $x$ hours can be represented by $y=3(2)^x$ . What does the 2 represent in this context?

a)

The initial amount of bacteria

b)

The rate of bacteria growth

c)

The new amount of bacteria

d)

Time in Hours

54.

A certain type of bacteria doubles in number every hour. If you start with 3 bacteria, the number of bacteria after $x$ hours can be represented by $y=3(2)^x$ . What does the y represent in this context?

a)

The initial amount of bacteria

b)

The rate of bacteria growth

c)

The new total of bacteria

d)

Time in Hours

55.

A car depreciates in value by 20% each year. If the initial value of the car is $25,000$ the value after x years can be represented by $y=25000\left(0.8\right)^x$ . The 25000 in the equation represents what in this context?

a)

The initial value of the car.

b)

The depreciation rate.

c)

The new value of the car.

d)

Time in years

56.

A certain species of fish has a population that triples every month. If the initial population is 200 fish, the population after $x$ months can be represented by $y=200(3)^x$ . What does the exponent (x) represent in this context?

a)

The initial population

b)

The monthly increase rate

c)

The number of months

d)

The final population

57.

A tree species grows in height by approximately 25% each year. If a sapling is initially 2 meters tall, the height after $x$ years can be represented by $y=2(1.25)^x$ . What does y represent in this context?

a)

The initial height

b)

The annual growth rate

c)

The number of years

d)

The new height

58.

A social media platform's user base increases by an exponential rate each month. The following equation represents the situation: $y=1000(1.1)^x$ . Based on the equation how many followers did they start with?

a)

1000

b)

1.1

c)

$x$

d)

$y$

59.

Does the following equation show growth or decay?
y=10,000*(0.76)^x

a)

Growth

b)

Decay

60.

The foundation of your house has about 1,200 termites. The termites grow at a rate of about 2.4% per day. How long until the number of termites doubles?

a)

29 to 30 days

b)

23 to 24 days

c)

15 to 16 days

d)

19 to 20 days

61.

Is this exponential growth or decay?

a)

Growth because a=1

b)

Decay because b=0.5

c)

Growth because there is no a

d)

Neither because a=0

62.

Pick the equation that is exponential growth

a)

y=2(0.5)^x

b)

y = 0.5(2)^x

c)

y = .5x - 2

d)

y = 2x + .5

63.

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

64.

What is a, the starting term, for the function: f(x) = 300(1.16)^x?

a)

300

b)

1.16

c)

.16

d)

x

65.

You buy a new computer for $2100. The computer decreases by 50% annually. How much is it worth after 2 years.

a)

225

b)

325

c)

425

d)

525

66.

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

67.

If the function f(x) = 4500(.75)^x, represents the amount of money John has left to pay on his school loans, what is the decay rate?

a)

4500

b)

.75

c)

75%

d)

25%

68.

Is the function: f(x) = 800(0.85)^x show growth or decay?

a)

Decay

b)

growth

c)

a line

d)

monkeys

69.

Does the function: f(x) = 200(.13)^x show growth or decay?

a)

Growth

b)

Decay

c)

It stays constant

d)

Bananas

70.

What is the percentage of decay for the following function f(x) = 200(.67)^x?

a)

200%

b)

67%

c)

33%

d)

x

71.

$y=$ (a) ( (b) ) $^x$

Write an exponential equation:

Represents exponential decay

Initial value of 150

Choose from the below words

300

0.70

70

1

5

72.

What is the equation of the horizontal asymptote for following exponential function?

a)

y = -4

b)

y > -4

c)

y < -4

d)

(0, -3)

73.

What is the equation of the horizontal asymptote for following exponential function?

a)

y = 1

b)

y = 2

c)

y > 1

d)

(0, 2)

74.

What is the asymptote of this function?

a)

y = 0

b)

y = 5

c)

y = 2

d)

y = 1

75.

Determine the horizontal asymptote for the function

f(x) = 3(2)^x-4+ 5

a)

x=4

b)

y=4

c)

x=5

d)

y=5

Alg Chapter 7 Review - Exponentials and logs

Total questions: 75

Worksheet time: 19hrs 45mins

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