Free Printable Unit 6 Review

1.

Rewrite log₂8 = 3 in exponential form

a)

2⁸ = 3

b)

2³ = 8

c)

3² = 8

d)

8³ = 2

2.

To evaluate a logarithm statement log₉81, you think "9 to what power is 81".

a)

True, and it's 2

b)

False

3.

log₅25 = ?

a)

2

b)

5

c)

125

4.

The base of common log is 10. So log 100 = ?

a)

1

b)

2

c)

10

d)

50

5.

Evaluate.
log₃81

a)

4

b)

¹/₄

c)

-4

d)

-¹/₄

6.

Log with a base "e" (log_e) is the same thing as...

a)

"e"

b)

Natural Logarithm (LN)

c)

Common Logarithm (Log)

d)

Natural Log, base "e"
LN_e

7.

Solve for x:

log₅(4x-7)=log₅(x+5)

a)

3

b)

12

c)

4

d)

7

8.

Solve for x:

log₄(3x-1)=log₄(2x+3)

a)

4

b)

3

c)

1

d)

8

9.

Solve for x:

log_x1000=3

a)

1

b)

10

c)

30

d)

3

10.

Using a calculator, solve for x:

2.8^x = 41

a)

0.277

b)

3.607

c)

-0.282

d)

3.684

11.

Solve for x:

log(x+6) = 1

a)

4

b)

4.222

c)

-5

d)

-9.550

12.

What is the domain of the graph?

a)

(-∞,∞)

b)

(-2, ∞)

c)

(0,∞)

d)

(-∞,2)

13.

What is the range of the graph?

a)

(-∞,∞)

b)

(-2, ∞)

c)

(0,∞)

d)

(-∞,2)

14.

What is the range of the graph?

a)

(-∞,∞)

b)

(2, ∞)

c)

(-3,∞)

d)

(0,-2)

15.

Is this function growth or decay?

a)

Growth

b)

Decay

16.

Is this function growth or decay?

a)

Growth

b)

Decay

17.

$f\left(x\right)=\left(\frac{1}{2}\right)^x$ Is this function growth or decay?

a)

Groeth

b)

Decay

18.

$f\left(x\right)=4\left(7\right)^x$ Is this function growth or decay?

a)

Growth

b)

Decay

19.

What trnasformations are happening to the exponential function?

a)

up 1

b)

right 2

c)

right 3

d)

down 2

e)

left 2

20.

Are f(x) and g(x) inverses based on the tables of values?

a)

yes, the inputs and outputs are switched

b)

no, the inputs and outputs should have opposite signs

c)

yes, the values are all positive

d)

no, the values are increasing

21.

A logarithmic function is the inverse of an exponential function. (a)

Choose from the below words

True

False

22.

Which equation is the inverse of the equation above?

a)

b)

c)

d)

23.

Which equation is the inverse of the equation above?

a)

b)

c)

d)

24.

Identify the asymptote of the transformed graph $y=\log_2\left(x+3\right)$ shown in red in the graph. #22

a)

$x=-3$

b)

$x=3$

c)

$y=3$

d)

$y=-3$

25.

The common logarithm has what base?

a)

10

b)

0

c)

e

d)

-e

26.

The inverse has been reflected over which line? (a)

Choose from the below words

y = x

y =1

y = 0

y = x + 1

27.

The natural logarithm has what base?

a)

10

b)

0

c)

e

d)

-e

28.

Logarithms are the inverse of ___________. #9

a)

Trees

b)

Quadratics

c)

Square

d)

Exponential

29.

What is the domain of the function shown? #31

a)

(-∞, ∞)

b)

(0, ∞)

c)

[1, ∞)

d)

(1, ∞)

30.

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 years?

a)

$827.52 (Mr. Williams)

b)

$831.10 (Mrs. Hoch)

c)

$839.45 (Mr. Krajunus)

d)

$846.80 (Ms. Palombo)

31.

Emily’s parents put $1,500 in her bank account for college tuition. At an interest rate of 8.25% compounded semiannually,what will be the balance after 18 years?

a)

$6,273.50 frustrated

b)

$6,314.08 bewildered

c)

$6,385.72 pleased

d)

$6,427.94 tickled pink

32.

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 interest will she earn in 10 years?

a)

$915.59 Rome

b)

$933.28 Sydney

c)

$979.81 Dublin

d)

$1,005.09 Paris

33.

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

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

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

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

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

34.

Chloe was studying earthquake waves in Japan. The function of $f\left(x\right)=354\left(1.15\right)^x$ gives the number of waves at the end of x days. What is the growth rate for this function?

a)

The initial number of waves is 15.

b)

The initial number of waves decreases at a rate of 85% each day.

c)

The initial number of waves increases at a rate of 15% each day.

d)

The number of waves at the end of one day is 354.

35.

This is an example of:

a)

Linear Growth

b)

Linear Decay

c)

Exponential Growth

d)

Exponential Decay

36.

Select all the equations that represent exponential decay.

a)

$y=\frac{1}{2}\left(4\right)^x$

b)

$y=4\left(\frac{1}{2}\right)^x$

c)

$y=80\left(1.4\right)^x$

d)

$y=60\left(0.7\right)^x$

e)

$y=3\left(0.6\right)^x$

37.

Please label each part of the function with the appropriate descricription.

a)

final value

b)

initial value

c)

growth/decay factor

d)

time

1

2

3

4

1)

2)

3)

4)

38.

Click on the part of the formula that represents the number of compounding periods per year.

A

B

C

D

E

39.

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

40.

What is the y-intercept of the function?

a)

2

b)

3

c)

1

d)

-2

41.

Using the change of base rule, what is this logarithm equivalent to?

a)

A

b)

B

c)

C

d)

D

42.

Using the change of base rule, what is this logarithm equivalent to?

a)

A

b)

B

c)

C

d)

D

43.

To solve 8 = 2^5x+7, you would need to re-write 8 as what base?

a)

8

b)

4

c)

2

d)

Cannot be determined

44.

Solve: 7^-x = 49

a)

x = 1

b)

x = -1

c)

x = 2

d)

x = -2

45.

Solve:
3^x-2= 27^4x

a)

-2/11

b)

-2/3

c)

2/11

d)

2/3

46.

Solve:

16^x-3 = 8^x-3

a)

9

b)

-3

c)

3

d)

0

47.

The population of a town is represented as $f\left(t\right)\ =\ 843,000\left(1.026\right)^x$

a)

The town grows at a rate of 26% annually.

b)

The town decays at a rate of 26% annually.

c)

The town decays at a rate of 2.6 % annually.

d)

The town grows at a rate of 2.6% annually.

48.

Simplify ln e³

a)

0

b)

e

c)

2

d)

3

49.

$5e^{8t}\ =\ 25$

Evaluate the above function.

a)

$8\ln\ 5\ =\ t$

b)

$\frac{1}{8}\ln\ 5\ =\ t$

c)

$8t\ =\ 5\ln x$

d)

$5\ln\ 8\ =\ t$

50.

A new model of iPad is made and sold 8450 units the first month. The sales have been decreasing by 8% each month since then. What equation can be used to calculate the number of iPads sold in any given month "t"? $f\left(t\right)\ =\$

(a)

51.

What is the common ratio for the sequence:
28, 14, 7, 3.5...

a)

2

b)

1/2

c)

-14

d)

-7

52.

Write the explicit formula for the following geometric sequence:

3, -12, 48, -192, ...

a)

a_n = 4(3)^n-1

b)

a_n = 3(4)^n-1

c)

a_n = -4(3)^n-1

d)

a_n = 3(-4)^n-1

53.

Find a₁₂ for the geometric sequence defined by the following formula:

a_n = 6(2)^n-1

a)

4096

b)

24,576

c)

2048

d)

12,288

Unit 6 Review

Total questions: 53

Worksheet time: 2hrs 46mins

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