Free Printable POA Chapter 6 Test Review

1.

Is the function exponential growth or decay? $y=5\left(1.82\right)^t$

a)

Exponential Growth

b)

Exponential Decay

2.

What is the percent rate of change? $y=5\left(1.82\right)^t$

a)

82% growth

b)

82% decay

c)

0.82% growth

d)

1.82% growth

3.

Is the function exponential growth or decay? $y=12\left(0.94\right)^t$

a)

Exponential Growth

b)

Exponential Decay

4.

What is the percent rate of change? $y=12\left(0.94\right)^t$

a)

6% growth

b)

6% decay

c)

94% growth

d)

94% decay

5.

Is the function exponential growth or decay? $y=6200\left(0.51\right)^t$

a)

Exponential Growth

b)

Exponential Decay

6.

What is the percent rate of change? $y=6200\left(0.51\right)^t$

a)

49% growth

b)

49% decay

c)

51% decay

d)

0.51% decay

7.

Is the function exponential growth or decay? $y=0.8\left(1.03\right)^t$

a)

Exponential Growth

b)

Exponential Decay

8.

What is the percent rate of change? $y=0.8\left(1.03\right)^t$

a)

1.03% growth

b)

97% decay

c)

0.03% growth

d)

3% growth

9.

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

a)

Rate of growth or decay

b)

Slope

c)

Initial value

d)

Exponent

10.

Does the function represent a growth or decay function?

a)

Exponential GROWTH

b)

Exponential DECAY

11.

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

a)

y = 15(35)^x

b)

y = 15(0.35)^x

c)

y = 35(1.15)^x

d)

y = 15(1.35)^x

12.

The value of a car you purchased for $20,000 decreases at a rate of 12% each year. What will the value of the car be after 3 years?

a)

$12,800.00

b)

$13,629.44

c)

$17,600.00

d)

$28,098.56

13.

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

a)

Rate of growth or decay

b)

Growth or Decay factor

c)

Initial value

d)

Exponent

14.

Determine the value of the decay rate for the function y = 56(0.45)^x?

a)

0.55

b)

0.45

c)

1.45

d)

1.55

15.

Given the function

$f\left(x\right)=\ 15000\left(0.85\right)^t$ , what is the percent rate of decrease?

a)

185%

b)

0%

c)

85%

d)

15%

16.

In the exponential growth function

$f\left(x\right)=25\left(1.5\right)^x$ , what is the initial value?

a)

1.5

b)

x

c)

25

d)

0.5

17.

Write each product using an exponent.

7 x 7 x 7 x 7 x 7 x 7 x 7 x 7

a)

7⁷

b)

7⁸

c)

8⁷

d)

7⁹

18.

Krystal was given $3,000 when she turned 2 years old. Her parents invested it at a 2% interest rate compounded annually which expression can be used to determine how much money Krystal had in the account when she turned 18?

a)

3000(1 + 0.02)¹⁶

b)

3000(1 + 0.02)¹⁸

c)

3000(1 - 0.02)¹⁶

d)

3000(1 - 0.02)¹⁸

19.

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.

a)

y=6(0.14)^x

b)

y=6(1+14)^x

c)

y=6(1.14)^x

d)

y=6(0.86)^x

20.

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

21.

Change 6.75% to a decimal.

a)

67.5

b)

.675

c)

675

d)

.0675

22.

A new savings account is opened with $400 and gains 3% every year. What is the exponential function?

a)

f(x)=400(1+3)^x

b)

f(x)=400(1-0.03)^x

c)

f(x)=400(1+0.03)^x

d)

f(x)=400(0.03)^x

23.

Simplify the exponential expression.

a)

2x⁶y¹²

b)

2x⁵y⁷

c)

8x⁶y¹²

d)

8x⁵y⁷

24.

Simplify the following exponential expression:
(3x⁴)(5x³)

a)

15x¹²

b)

8x⁷

c)

8x¹²

d)

15x⁷

25.

Simplify the exponential expression:

a)

10x^-2

b)

2x²

c)

2x¹²

d)

10x¹²

26.

The function y = 24,220 (0.85)^x represents Mr. Bittle's investment in the stock exchange where x is measured in months.

Which statement is NOT true.

a)

Mr. Bittle loses 85% of his investment monthly

b)

Mr. Bittle initially invested $24,220

c)

Each month Mr. Bittle loses 15% of his investment

27.

Write an exponential function to model the situation. The value of a car is $18000 and is depreciating at a rate of 12% per year.

a)

V(t) = .88(18000)^t

b)

V(t) = .12(18000)^t

c)

V(t) = 18000(.88)^t

d)

V(t) = 18000(.12)^t

28.

What is the a-value (or y-intercept) for the function: f(x) = 800(0.85)^x?

a)

800

b)

0.85

c)

0.15

d)

x

29.

Simplify.

Simplificar.

(x⁴) (x)

a)

2x⁴

b)

x

c)

x⁵

d)

x⁴

30.

Solve using the product law of exponents and simplify your answer.

Resolver utilizando la ley de productos de los exponentes y simplifica tu respuesta.

(m)(m⁶)(m^-2)

a)

m^-12

b)

m⁵

c)

m⁴

d)

m⁹

31.

Write with positive exponents:

1/a^-2

a)

a^-2

b)

a²

c)

1/a¹

32.

-4x⁰

a)

-4x

b)

-4

c)

1

d)

-1

33.

(5³x²y⁴)⁰

a)

5xy

b)

1

c)

0

d)

5

34.

Simplify

(2a²b⁴z)(6a³b²z⁵)

a)

8a⁵b⁶z⁶

b)

12a⁶b⁸z⁵

c)

12a⁵b⁶z⁶

d)

8a⁶b⁸z⁵

35.

a)

b)

c)

d)

36.

x^-3

a)

-x³

b)

1 / x³

c)

1 / x^-3

d)

-x^-3

37.

a)

b)

c)

d)

38.

x⁶ / x²

a)

x⁴

b)

x¹²

c)

x³

d)

x⁸

39.

When dividing powers with the same base, you _______________ the exponents.

a)

Add

b)

Subtract

c)

Multiply

d)

Divide

40.

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

a)

add

b)

subtract

c)

multiply

d)

divide

41.

Simplify the expression:
c⁴⋅c³=

a)

^c12

b)

c⁴⁺³

c)

c⁷

42.

$\left(9y\right)^3$

a)

$9y^3$

b)

$9^3y$

c)

$27y^3$

d)

$729y^3$

43.

Simplify the expression using exponential notation:

$\left(a^4\right)^3$

a)

$a^{12}$

b)

$a^7$

c)

$a$

d)

$a^{15}$

44.

According to exponent rules, when we multiply powers we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

45.

(2x³y)⁶

a)

2x¹⁸y⁶

b)

64x¹⁸y⁶

c)

64x³y⁶

d)

2x³y⁶

46.

n⁴⋅n⁷

a)

n¹¹

b)

n4

c)

n²⁸

d)

n7

47.

8⁷ ⁄ 8²

a)

8⁵

b)

8⁹

c)

8¹⁴

d)

1⁵

48.

Simplify the following expression:
xy^-7

a)

xy⁷

b)

x/y⁷

c)

x⁷/y

d)

x⁷y

49.

a)

a⁸b¹³

b)

a²b⁷

c)

a¹⁵b³⁰

50.

Write the following expression in radical form:

a)

a.)

b)

b.)

c)

c.)

d)

d.)

51.

a)

7³

b)

7

c)

7^3/4

d)

7^4/3

52.

Re-write the expression in radical form.
x^2/3

a)

∛x²

b)

√x³

c)

(1/x)

d)

∛x

53.

a)

2^1/6

b)

64

c)

6^1/2

d)

2⁶

54.

Simplify
x⁴⋅x³⋅x

a)

x⁸

b)

x¹²

c)

x⁷

d)

x¹⁰

55.

Simplify

a)

x¹²

b)

x¹⁷

c)

x⁶

d)

x²³

56.

Simplify

a)

z

b)

z¹²

c)

1

d)

z¹⁴

57.

Simplify

a)

z¹⁵

b)

z⁸

c)

z³

d)

z¹¹

58.

Simplify

a)

w²⁴y⁹

b)

w¹¹y⁶

c)

y³/w⁶

d)

w⁶/y³

59.

Simplify $2xy\ \cdot4yx^2$

a)

$4\ y^2x$

b)

$8x^3y^3$

c)

$8x^3y^2$

60.

Simplify $\frac{4\ x^5y^7}{2x^2y}$

a)

$2x^2y$

b)

$2x^3y^6$

c)

$2x^2y^5$

d)

$2x^7y^8$

61.

Simplify $4x^2y^3\ \cdot4x^3$

a)

$16x^5y^3$

b)

$16x^5y^2$

c)

$16x^4y^3$

d)

$16x^2y^2$

62.

Combine like terms -5v⁴ - 5v² + 8v - 6v² - 3v⁴

a)

-10v⁴+8v

b)

-8v⁴ +11v² + 8v

c)

-8v⁴ - 11v² + 8v

d)

8v⁴ - 11v² - 8v

63.

Simplify 8x² - 6x - 8x² - 6x⁴ - 7x

a)

-6x⁴ - 13x

b)

6x⁴ - 13x²

c)

-6x⁴ - x

d)

8x² - x

64.

a)

2a²b⁶

b)

1/2a²b⁶

c)

b⁶/2a²

d)

2b⁶/a²

65.

a)

$-8xy^7$

b)

$-32x^2y^{10}$

c)

$32x^{10}y^2$

d)

$16x^2y^{10}$

66.

$\frac{x^{-2}}{x^{-10}y^{-8}}$

a)

$\frac{x^8}{y^{-8}}$

b)

$x^{20}y^8$

c)

$x^8y^8$

d)

$\frac{x^{10}y^8}{x^2}$

67.

$\left(\frac{3m^2n^7}{m}\right)^5$

a)

$15m^7n^{12}$

b)

$243m^5n^{35}$

c)

$15m^{15}n^{35}$

d)

$243m^7n^{12}$

68.

Simplify the expression

a)

$\frac{-1}{3x^5y^7}$

b)

$3x^5y^7$

c)

$16x^{13}y^9$

d)

$\frac{1}{16x^{13}y^9}$

69.

How would you write 564,000,000 in scientific notation?

a)

5.64 x 10^-7

b)

5.64 x 10⁶

c)

5.64 x 10⁸

d)

56.4 x 10⁷

70.

Express the following in scientific notation:
.000457

a)

457 x 10⁶

b)

457 x 10^-6

c)

4.57 x10⁴

d)

4.57 x 10^-4

POA Chapter 6 Test Review

Total questions: 70

Worksheet time: 3hrs 27mins

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