Free Printable Review Chapter 6

1.

Is this exponential growth or decay?

a)

Growth

b)

Decay

2.

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

a)

Exponential Growth

b)

Exponential Decay

c)

Linear

d)

None of the above

3.

What is the base in
f(x)=2(6)^x+3-8 ?

a)

2

b)

6

c)

-3

d)

-8

4.

Using the parent function y=3^x what would the graph of y=3^x+1 look like?

a)

Horizontal shift left one unit!

b)

Horizontal shift right one unit!

c)

Vertical shift up one unit!

d)

Vertical shift down one unit!

5.

Using the parent function y=3^x what would the graph of y=3^x+1 look like?

a)

Horizontal Shift to the right 1 unit

b)

Horizontal shift to the left one unit

c)

Vertical shift one unit up

d)

Vertical shift one unit down

6.

Describe the transformations for the following function:

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

a)

2 units right and 4 units up

b)

4 units to the left and 2 units up

c)

2 unit right and 4 units down

d)

2 units left and 4 units down

7.

Which statement about the graph of

y=8(0.25)^x

is true?

a)

The coordinates of the x-intercept are (0.25,0)

b)

The coordinates of the y-intercept are (0,8)

c)

The equation of the asymptote is x=0

d)

The graph includes the point (2,1)

8.

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

a)

Growth

b)

Decay

c)

Linear

d)

None

9.

Which function represents the table of values?

a)

f(x) = 4x

b)

f(x) = x³

c)

f(x) = 4^x

d)

f(x) = 4^x-1

10.

Convert 3% to a decimal

a)

3

b)

.3

c)

.03

d)

.003

11.

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

12.

The population of the United States was 248,718,301 in 1990 and was projected to grow at a rate of about 8% per decade. Predict the population, to the nearest hundred thousand, for the years 2018.

a)

978617180000 people

b)

248757647 people

c)

993883180 people

d)

55448350 people

13.

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

14.

Daniel’s Print Shop purchased a new printer for $35,000. Each year it depreciates at a rate of 5%. How much will the printer be worth in 8 years?

a)

$23,219.72

b)

$136.72

c)

$51,710.94

d)

$16,710.94

15.

What does Hakuna Matata mean?

a)

Live for the Moment

b)

Circle of Life

c)

Bless You

d)

No worries

16.

What does the "r" represent in the exponential model $f\left(x\right)=a\left(1-r\right)^x$

a)

rate of decay as a decimal

b)

rate of growth as a decimal

17.

The original value of a painting is $1400, and the value increases by 9% each year. Write an exponential growth function to model this situation.

a)

y=1400(1.09)^x

b)

y=1.09(1400)^x

c)

y=1400(.91)^x

d)

y=1.09^x

18.

The population of Winnemucca, Nevada, can be modeled by P=6191(1.04)^twhere t is the number of years since 1990. What was the population in 1990?

a)

0 people

b)

It doesn't say

c)

I don't know

d)

6191

19.

Semi-Annually means how many times a year?

a)

4

b)

2

c)

1

d)

6

20.

Find the balance in the account after the given period.

$5000 deposit earning 1.5% compounded quarterly after 3 years

a)

$5,229.70

b)

$7,604.38

c)

$7,777.27

d)

$5,538.86

21.

Principal: $5000
Interest Rate: 3.75%
Time: 25 years
Compounded Monthly
State the future account balance.

a)

$12712.31

b)

$12,749.30

c)

$12,657.59

d)

$12550.84

22.

You borrowed $59,000 for 2 years at 11% which was compounded annually. What total will you pay back?

a)

$13,693.90

b)

$1,363.90

c)

$72,693.90

d)

$73,793.90

23.

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

24.

What does the r stand for in this formula?

a)

Initial amount

b)

Final amount

c)

Rate

d)

Time

e)

The number of times compounded per year

25.

What does the P stand for in this formula?

a)

Initial amount

b)

Final amount

c)

Rate

d)

Time

e)

The number of times compounded per year

26.

Kimi invests $4,000 at 3% interest compounded continuously. How much money will she have in 4 years?

(a)

27.

Dash invested $10,000 at 3% interest compounded continuously. How much will he have after 8 years?

(a)

28.

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

29.

Change 32% into a decimal.

a)

32

b)

3.2

c)

.32

d)

.032

30.

Mr. T invested $15,000 in an account that pays 5% interest compounding continuously, how much is in the account after 5 years?

a)

$15,500.50

b)

$19,260.38

c)

$19,260.40

d)

$21,500.25

31.

What does the r stand for in this formula?

a)

Rate as a percent

b)

Rate as a decimal

c)

number of times interest is compounded

32.

What does the t stand for in this formula?

a)

time in weeks

b)

time in months

c)

time in years

d)

the number of times interest is compounded per year

33.

The formula below can be used to determine the total amount of money in a savings account. What was the initial amount of money deposited in the account?

$A=3250e^{0.062\cdot8}$

(a)

34.

The formula below can be used to determine the total amount of money in a savings account. What is the interest rate as a percent?

$A=3250e^{0.062\cdot8}$

(a)

35.

The formula below can be used to determine the total amount of money in a savings account. How long was the money left in the account?

$A=3250e^{0.062\cdot8}$

(a)

36.

Logarithms are the inverse of ___________.

a)

Trees

b)

Quadratics

c)

Square

d)

Exponential

37.

How are exponentials and logarithms related?

a)

They're cousins

b)

They're inverses

c)

They're not related

d)

They're reciprocals

38.

When you want to find the inverse of a function, you first

a)

Solve for y

b)

Change to exponential form

c)

Switch x and y

d)

Change to logarithmic form

39.

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

40.

Find the inverse of $y=\ln\left(x+3\right)$

a)

$y=e^x-3$

b)

$y=e^{x-3}$

c)

$y=e^x+3$

d)

$y=e^{x+3}$

41.

Rewrite as an exponential: log₂8 = 3

a)

3² = 8

b)

2³ = 8

c)

2⁸ = 3

d)

8³ = 2

42.

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)

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

43.

Find x: log₅(x) = 0

a)

No Solution

b)

x = 0

c)

x = 5

d)

x = 1

44.

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

a)

x = -1

b)

x = 1

c)

x = 0

d)

No Solution

45.

Rewrite as a log: 7⁰ = 1

a)

log₇(1) = 0

b)

log₀(7) = 1

c)

log₇(0) = 1

d)

log₁(0) = 7

46.

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

47.

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

48.

Please rate your confidence level in converting exponentials and logarithms:

a)

I don't know what I am doing

b)

I'm starting to understand, but need more practice

c)

I'm ready to move on and learn more about logarithms.

49.

Evaluate log₅20 to the third decimal place

a)

0.537

b)

2.996

c)

1.301

d)

1.861

50.

a)

log (xy³)

b)

log (x⁶− y³)

c)

log (x⁶/y³)

d)

log (x⁶ + y³)

51.

log(xy²)

a)

logx+2logy

b)

logx+logy²

c)

logx-2logy

d)

logx+logy+log2

52.

log(4x)

a)

log4-logx

b)

log4+logx

c)

4logx

d)

xlog4

53.

Rewrite log_pt = m in exponential form.

a)

p^t = m

b)

t^m = p

c)

m^t = p

d)

p^m = t

54.

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

55.

$\log\left(\frac{m^3}{n}\right)$

a)

logm-log3-logn

b)

3logm+logn

c)

3logm-logn

d)

3log(m-n)

56.

$\log\left(\frac{8x}{yz}\right)\$

a)

log8+logx-logy-logz

b)

log8+logx-logy+logz

c)

log(8x)-log(yz)

d)

8logx-ylogz

57.

When you have two log expressions separated by a plus sign (+), we really need to ___________ them to simplify into one log expression.

a)

add

b)

subtract

c)

multiply

d)

divide

58.

When you have two log expressions separated by a minus sign (-), we really need to ___________ them to simplify into one log expression.

a)

add

b)

subtract

c)

multiply

d)

divide

59.

Evaluate:

\log_264

(a)

60.

Evaluate: $\log_{10}100,000$

(a)

61.

Solve:

\log_3\left(4x-17\right)=5

(a)

62.

Solve for b:
4^{3b - 3} = 1/16

a)

7

b)

-1/4

c)

1/2

d)

1/3

63.

Solve for p:
4^p+2 = 64

a)

-16/9

b)

1

c)

8

d)

7/6

64.

Solve the following exponential equation:

3^3=3^{4x+2}

a)

$x=\frac{1}{4}$

b)

$x=-\frac{1}{4}$

c)

$x=\frac{1}{2}$

d)

$x=-\frac{1}{2}$

65.

Solve the following exponential equation:
$\left(\frac{1}{2}\right)^{2x}=4^3$

a)

$x=3$

b)

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

c)

$x=-3$

d)

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

66.

Evaluate: $15^0=x$

a)

No Solution

b)

1

c)

0

d)

15

67.

Name the base in the power below:
$8^{-2}$

a)

Base is -2

b)

Base is 0

c)

Base is 1

d)

Base is 8

e)

Base is 1/8

68.

Solve the equation for x.

a)

x = 2

b)

x = 3

c)

x = 8

d)

x = 64

69.

Solve: 7^-x = 49

a)

1

b)

-1

c)

2

d)

-2

70.

Write in exponential form: ∛4⁵

a)

4^3/5

b)

4^5/3

c)

4^1/5

d)

4^1/3

71.

log₂(x+3)=4

a)

16

b)

13

c)

3

d)

10

72.

log_x1000=3

a)

1

b)

10

c)

30

d)

3

73.

Solve for x:

log(x+6) = 1

a)

4

b)

4.222

c)

-5

d)

-9.550

Review Chapter 6

Total questions: 73

Worksheet time: 8hrs 13mins

Similar Resources on Wayground