Free Printable Chapter 7 Exponentials and Logarithms Review

1.

Identify the y-intercept (initial value) in the function f(x)=13(.27)^x

a)

(.27)^x

b)

0,.27

c)

0,13

d)

0,3.51

2.

What is the y-intercept of the function?

a)

0,2

b)

0,3

c)

0,1

d)

0,-2

3.

Classify the model as Exponential GROWTH or DECAY.

$A=10(1.01)^3$

a)

Growth $y=a\left(1+r\right)^t$

b)

Decay $y=a\left(1-r\right)^t$

4.

How do you know that this was exponential decay? $f\left(x\right)=\ 25\ \left(\ 0.20\right)^x$

a)

Because the 25 was bigger than one

b)

Because the 0.20 was bigger than one

c)

Because the 25 was less than one

d)

Because the 0.20 was less than one

5.

What is the transformation?

a)

Vertical Translation up 2

b)

Vertical Translation down 2

c)

Horizontal Translation left 2

d)

Horizontal Translation right 2

6.

What is the transformation?

a)

Vertical Translation up 1

b)

Vertical Translation down 1

c)

Horizontal Translation left 1

d)

Horizontal Translation right 1

7.

How did the graph transform from the parent function?

y=-(2)^(x)

a)

Down 5

b)

Vertical Stretch by 5

c)

Left 2

d)

Right 2

e)

Flipped/Reflected over the x-axis

8.

You buy a car for $8000 that depreciates at a rate of 11% a year. How much is the car worth after 5 years?

Round to the nearest cent. (two decimal places)

(a)

9.

You start an account with $500 and an interest rate of 6% compounded monthly. How much is in the account after 3 years?

Round to the nearest cent. (two decimal places)

(a)

10.

North Dakota has recently had the fastest growing population out of all 50 states. On Jan 1, 2013, the population of North Dakota was 700,000 people. North Dakota’s population has been growing by 5% per year. Express North Dakota’s population, N, in terms of years since 2013, t.

Check the BEST answer:

a)

N=700,000(1.05)^t

b)

N=700,000(1.5)t

c)

N=700,000(1-0.05)^t

d)

N=700,000(0.95)^t

11.

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

12.

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

(a)

13.

Write in exponential form:

log ₂ 32 = 5

a)

2⁵ = 32

b)

5² = 32

c)

5³² = 2

d)

2³² = 5

14.

Write in exponential form:
log ₃₆ 1 = 0

a)

36⁰ = 1

b)

36¹ = 0

c)

1³⁶ = 0

d)

1⁰ = 36

15.

Write in logarithmic form:
9² = 81

a)

log ₉ 81 = 2

b)

log ₂ 81 = 9

c)

log ₉ 2 = 81

d)

log ₂ 9 = 81

16.

Write in logarithmic form:
4⁵ = 1024

a)

log ₄ 1024 = 5

b)

log ₅ 1024 = 4

c)

log ₄ 5 = 1024

d)

log ₅ 4 = 1024

17.

Evaluate log₅25 = x

a)

2

b)

5

c)

125

18.

evaluate log₂ 16

a)

8

b)

4

c)

-4

d)

2

19.

evaluate log₉ 3

a)

2

b)

-2

c)

1/2

d)

0

20.

Expand

a)

A

b)

B

c)

C

d)

D

21.

Condense

a)

log₈x³y⁹

b)

log₈(x³/y⁹)

22.

Condense

a)

4log₃x-4log₃y

b)

log₃(x⁴/y⁴)

c)

log₃(x⁴y⁴)

d)

log₃(x⁴) - log₃(y⁴)

23.

log(xy²)

a)

logx+2logy

b)

logx+logy²

c)

logx-2logy

d)

logx+logy+log2

24.

Choose the correctly condensed logarithm

$2\log_3u-\log_3z$

a)

$2\log_3\left(\frac{u}{z}\right)$

b)

$\log_3\left(\frac{u^2}{z}\right)$

c)

$\log_3\left(u^2-z\right)\ \$

d)

$2\log_3\left(u-z\right)$

25.

Choose the correctly condensed common logarithm

$\log x+\log y+3\log z$

a)

$\log\left(xyz^3\right)$

b)

$\log\left(xyz\right)^3\ \ \ \$

c)

$\log\left(3xyz\right)\ \ \ \ \$

d)

$3\log\left(xyz\right)$

26.

Condense: $4\log p+2\log q-3\log r$

a)

$\log\ p^4q^2r^3$

b)

$\log\ \frac{p^4}{q^2r^3}$

c)

$\log\ \frac{8pq}{3r}$

d)

$\log\ \frac{p^4q^2}{r^3}$

27.

Solve: $3^{2x-6}=81\$

a)

$6$

b)

$-1,\ 3$

c)

$5$

d)

$7.5$

28.

Solve:

2^x=5

a)

$\log_25$

b)

$\log_52$

c)

$\ln5$

d)

$\ln2^5$

29.

Solve:

2log₆(x-8)=2

a)

14

b)

81/8

c)

18

d)

9969

30.

Solve:

log₂(x + 3)=5

a)

x=2

b)

x=29

c)

x=7

d)

x=32

31.

Solve.

2(16^x+6) - 8 = 35

a)

-4.67

b)

-4.89

c)

-2.93

d)

-2.95

32.

Solve:

log₆(2x + 3) = 3

a)

x = 106.5

b)

x = 100

c)

x = 16

d)

x = 50

Chapter 7 Exponentials and Logarithms Review

Total questions: 32

Worksheet time: 1hrs 11mins

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