Free Printable M3 U2 Unit Review

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M3 U2 Unit Review

Total questions: 50

Worksheet time: 3hrs 56mins

Name

Class

Date

In an exponential function, what does the 'a' represent?

Future Value

Time

Initial Quantity

Growth or Decay Factor

In an exponential function, what does the 'b' represent?

Future Value

Time

Initial Quantity

Growth or Decay Factor

In an exponential function, what does the 'y' represent?

Future Value

Time

Initial Quantity

Growth or Decay Factor

In an exponential function, what does the 'x' represent?

Future Value

Time

Initial Quantity

Growth or Decay Factor

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

300

1.16

.16

What is b, the growth factor, for the function: f(x) = 300(1.16)^x?

300

1.16

.16

A population of 2200 beetles is too large to sustain and decreases in population each month at a rate of 5%. How would you write your decay factor, b?

-5

-.05

.95

.05

The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the decay factor?

^.08

^1.08

.92

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

y = 15(35)^x

y = 15(1.35)^x

y = 15(0.35)^x

y = 35(1.15)^x

10.

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

Growth

Decay

11.

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

Exponential Growth

Exponential Decay

Linear

None

12.

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

Exponential Growth

Exponential Decay

Linear

None of the above

13.

Write an equation that models the following situation:
Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.

y=6(0.14)^x

y=6(1+14)^x

y=6(1.14)^x

y=6(0.86)^x

14.

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

y=5000(0.7)^x

y=30(5000)^x

y=5000(1.3)^x

y=5000x^x

15.

A population is decreasing by 9% each year. How would you determine the decay factor?

(1 + 0.09) = 1.09

(1 - 0.09) = 0.91

(1 + 0.9) = 1.9

(1 - 0.9) = 0.1

16.

Semi-Annually means how many times a year?

17.

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.

Equation: A = P (1 + r/n)^nt

$15,415.94

$15,683.28

$15,927.56

$16,109.05

18.

Principal: $5000

Interest Rate: 3.75%

Time: 25 years

Compounded Monthly

State the future account balance.

Equation: A = P (1 + r/n)^nt

$12712.31

$12,749.30

$12,657.59

$12550.84

19.

What does A represent in the above formula?

The starting amount of money

The end amount of money

The interest rate amount

The amount of time

The number of times money is compounded each year

20.

What does P represent in the above formula?

The starting amount of money

The end amount of money

The interest rate amount

The amount of time

The number of times money is compounded each year

21.

What does r represent in the above formula?

The starting amount of money

The end amount of money

The interest rate amount

The amount of time

The number of times money is compounded each year

22.

What does n represent in the above formula?

The starting amount of money

The end amount of money

The interest rate amount

The amount of time

The number of times money is compounded each year

23.

What does t represent in the above formula?

The starting amount of money

The end amount of money

The interest rate amount

The amount of time

The number of times money is compounded each year

24.

Rewrite 3⁴ = 81 in logarithmic form.

log₃4 = 81

log₈₁3 = 4

log₃81 = 4

log₄81 = 3

25.

Change to exponential form.

log_a2 = 5

a²= 5

5² = a

a⁵= 2

2⁵ = a

26.

Change to logarithmic form.

3^h = w

log_w3 = h

log₃w = h

log_h3 = w

log₃h = w

27.

Rewrite log₂8 = 3 in exponential form.

2⁸ = 3

2³ = 8

3² = 8

8³ = 2

28.

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

Equation: A = P e^rt

$1,225,54

$2,225.54

$22,255.40

$225.54

29.

You desire to have One Million dollars in 25 years. How much money would you need to invest today at 12% interest if it is compounded continuously?

Equation: A = P e^rt

$40,000

$33,333

$49,787

$100,000

30.

Solve: 7^-x = 49

x = 1

x = -1

x = 2

x = -2

31.

Solve: 2^x = 4^x+1

x = -2

x = 2

x = -3

x = 3

32.

Sovle for x:

5^{-3x - 1} = 25

x = -1

x = -4

x = -3

x =1

33.

Solve for x.
log₇70=log₇(10x-30)

x=1

x=2

x=10

x=-2

34.

ln(9x-2)=ln(x+14)

x=2

x=.156

x=-3

x=0

35.

log₂x=4

x=8

x=16

Does Not Exist

x=.546

36.

e^t=3

1.237

-2.337

1.099

0.475

37.

x = 2

x = 29

x = 7

x = 32

38.

Solve

-20

39.

Solve 5 ln x = 35

about 1096.63

about 1086.63

about 1096.36

about 1046.11

40.

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

"e"

Natural Logarithm (LN)

Common Logarithm (Log)

Natural Log, base "e"
LN_e

41.

log(x+6) = 1

4.222

-5

-9.550

42.

What is the y-intercept of the function?

-2

43.

What is the asymptote of the graph?

x=2

y=-2

y=0

y=-1

44.

What is the asymptote?

y=0

x=2

y=1

x=0

45.

Classify the following graph.

Exponential Growth

Exponential Decay

Logarithmic

46.

Where is the asymptote?

x = 1

y = 1

x = -1

y = -1

47.

List the range for the following.

(-∞,∞)

(-1, ∞)

(5,∞)

(1, ∞)

48.

List the domain for the following.

(-2, ∞)

(-∞, ∞)

(- ∞,4)

(1/5, ∞)

49.

What is the domain?

(-∞, ∞)

(0, ∞)

[1, ∞)

(1, ∞)

50.

Match the graph with its equation

y = log₄ (x)+2

y = log₄ (x + 2) + 1

y = log₄ (x - 1) + 2

y = log₄ (-x + 2)

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M3 U2 Unit Review

Total questions: 50

Worksheet time: 3hrs 56mins

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