Quiz about Unit 9 Retake Exponential and Logarithmic Functions

Question 1

solve for x.

$$2^x=2^{3x-4}$$

Accepted Answer

2

Answer

-2

Answer

1/2

Answer

4/3

Question 2

solve for x.

$$25^{x+3}=5^{5x-9}$$

Accepted Answer

5

Answer

1

Answer

4

Answer

3

Question 3

Solve for p:
4^p+2 = 64

Accepted Answer

1

Answer

-16/9

Answer

8

Answer

7/6

Question 4

32 = 9

Accepted Answer

log ₃ 9 = 2

Answer

log ₃ 2 = 9

Answer

log ₉ 3 = 2

Answer

log ₂ 9 = 3

Question 5

25 = 32

Accepted Answer

log ₂ 32 = 5

Answer

log ₅ 32 = 2

Answer

log ₃₂ 5 = 2

Answer

log ₂ 5 = 32

Question 6

bk = m

Accepted Answer

log _b m = k

Answer

log _m k = b

Answer

log _b k = m

Answer

log _k m = b

Question 7

e3 = 20.1

Accepted Answer

ln 20.1 = 3

Answer

ln 20.1 = e

Answer

ln 3 = 20.1

Answer

ln e = 20.1

Question 8

10³ = 1000

Accepted Answer

log 1000 = 3

Answer

log ₁₀₀₀ 3 = 10

Answer

log ₃10 = 1000

Answer

log 3 = 1000

Question 9

Write in exponential form.
log₂32 = 5

Accepted Answer

25 = 32

Answer

2-5 = 32

Answer

232 = 5

Answer

325 = 2

Question 10

Change to Exponential Form:
log₆36 = 2

Accepted Answer

62=36

Answer

26=36

Answer

362=6

Answer

366=2

Question 11

Rewrite log_pt = m in exponential form.

Accepted Answer

pm = t

Answer

pt = m

Answer

tm = p

Answer

mt = p

Question 12

Rewrite this equation in logarithmic form.

Accepted Answer

Option C is correct

Answer

A.

Answer

B.

Answer

D.

Question 13

e3 = 20.1

Accepted Answer

ln 20.1 = 3

Answer

ln 20.1 = e

Answer

ln 3 = 20.1

Answer

ln e = 20.1

Question 14

Expand: $$\log_6\left(\frac{5}{4y}\right)$$

Accepted Answer

$$\log_65\ -\ \log_64\ -\ \log_6y$$

Answer

$$\log_65\ +\ \log_64\ +\ \log_6y$$

Answer

$$\log_65\ -\ \log_64\ +\ \log_6y$$

Answer

$$\log_65\ -\ \log_64y$$

Question 15

Expand: $$\log_4\left(3x^2\right)$$

Accepted Answer

$$\log_43\ +\ 2\log_4x$$

Answer

$$2\log_43x$$

Answer

$$2\log_43\ +\ 2\log_4x$$

Answer

$$2\log_43\ +\ \log_4x$$

Question 16

Condense the Logarithm $$5\log_{ }a\ -\ 25\log_{ }b$$

Accepted Answer

$$\log_{ }\ \left(\frac{a^5}{b^{25}}\right)$$

Answer

$$\log\ \left(a^5+b^{25}\right)$$

Answer

$$\log\ \left(a^5-b^{25}\right)$$

Answer

$$\log\ \left(ab\right)^{25}$$

Question 17

Condense $$3\log_{ }x+4\log_{ }y\ +\log_{ }z$$

Accepted Answer

$$\log_{ }\ x^3y^4z$$

Answer

$$12\log_{ }\ xyz$$

Answer

$$\log_{ }\ 3x4yz$$

Answer

logx³y³z³

Question 18

Simplify: $$2\log_3\left(11x\right)$$

Accepted Answer

$$\log_3\left(121x^2\right)$$

Answer

$$\log_3\left(22x\right)$$

Answer

$$\log_3\left(121x\right)$$

Answer

$$\log_3\left(11x^2\right)$$

Question 19

Simplify: $$\frac{1}{2}\log_964+\log_9x$$

Accepted Answer

$$\log_98x$$

Answer

$$\log_9\left(32x\right)$$

Answer

$$\log_9\left(8x\right)$$

Answer

$$\log_9\left(\frac{8}{x}\right)$$

Question 20

Expand using the properties of Logaritms $$\log_{ }\ \frac{x^3}{y^4z}$$

Accepted Answer

$$3\log_{ }x-4\log_{ }y\ -\log_{ }z$$

Answer

$$\log_{ }x+4\log_{ }y\ +\log_{ }z$$

Answer

$$3\log_{ }x+4\log_{ }y\ +\log_{ }z$$

Answer

$$3\log_{ }x-4\log_{ }y\ +\log_{ }z$$

Question 21

log(2x) - log(5) = log(30)

Accepted Answer

75

Answer

6/5

Answer

45/2

Answer

-3/8

Question 22

log(4x) - log(4) = log(12)

Accepted Answer

12

Answer

4

Answer

10

Answer

100

Question 23

Solve

Accepted Answer

8

Answer

-8

Answer

1/8

Answer

-1/8

Question 24

Question 24.

Accepted Answer

84

Answer

5

Answer

13

Answer

-20

Question 25

Solve

Accepted Answer

A

Answer

B

Answer

C

Answer

D

Question 26

$e^{a+1}=65$

Solve the equation for the missing variable. Be sure to check for extraneous solutions.

Accepted Answer

a = 3.17

Answer

a = 2.94

Answer

a = 1.42

Answer

a = 0.89

Question 27

The number of turkey vultures in a nature sanctuary is doubling each year. When the sanctuary opened, it was home to 204 turkey vultures. Which equation can be used to find the number of turkey vultures after x years?

Accepted Answer

$$y=204\left(2\right)^x$$

Answer

$$y=204\left(x\right)^2$$

Answer

$$y=2\left(204\right)^x$$

Answer

$$y=x\left(2\right)^{204}$$

Question 28

A population of ants increases by a factor of 5 each year. Initially there were 450 aunts. Which equation represents the amount of aunts after 9 years?

Let y represent the total amount of aunts after x years.

Accepted Answer

$$y=450\left(5\right)^9$$

Answer

$$y=450\left(9\right)^5$$

Answer

$$y=5\left(450\right)^9$$

Answer

$$y=9\left(450\right)^5$$

Question 29

You have inherited land that was purchased for $30,000 in 1960. The value of the land increased by approximately 5% per year. Write an equation to represent the situation:

Accepted Answer

$$f\left(x\right)\ =\ 30,000\left(1\ +\ 0.05\right)^t$$

Answer

$$f\left(x\right)\ =\ 30,000\left(1\ -\ 0.05\right)^t$$

Question 30

Is y = 54(.20)^x growth or decay?

Accepted Answer

Decay because of the .20

Answer

Growth because of the 54

Answer

Decay because of the 54

Answer

Growth because of the .20

Question 31

The population of Winnemucca, Nevada, can be modeled by P=6191(1.04)^t where t is the number of years since 1990. What percent did the population increase each year?

Accepted Answer

4%

Answer

104%

Answer

40%

Answer

400%

Question 32

A sailboat that costs $5,950 decreases in value by 11% per year. How much will the boat be worth after 6 years?

Accepted Answer

$2,957.04

Answer

$5,884.00

Answer

$5,178.97

Answer

$2,992.96

Question 33

You bought a brand new car for $45,000. The car depreciates at approximately 7% per year. How much will the car be worth after 8 years? Round to the nearest whole dollar.

Accepted Answer

$25,181

Answer

$77,318

Answer

$41,850

Answer

The value won't change at all.

Question 34

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?

Accepted Answer

9766

Answer

9765

Answer

9006

Answer

5433

Question 35

You buy a new computer for $2100. The computer decreases by 50% annually. When will the computer have a value of $600?

Accepted Answer

between 1 and two years

Answer

more than 5 years

Answer

less than a year

Answer

between 3 and 4 years

Question 36

You drink a beverage with 120 mg of caffeine. Each hour, the caffeine in your system decreases by about 12%. How long until you have 10mg of caffeine?

Accepted Answer

19 to 20 hours

Answer

10 to 20 hours

Answer

15 to 16 hours

Answer

5 to 6 hours

Question 37

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

Accepted Answer

y=15,000(0.92)^x

Answer

y=8(15,000)^x

Answer

y=15,000(1.08)^x

Answer

y=15,000(0.08)^x

Question 38

Is this exponential growth or decay?

Accepted Answer

Decay because b=0.5

Answer

Growth because a=1

Answer

Growth because there is no a

Answer

Neither because a=0

Question 39

In 1985, there were 285 cell phone subscribers in the small town of Centerville. The number of subscribers increased by 75% per year after 1985. How many cell phone subscribers were in Centerville in 1994?

Accepted Answer

43871

Answer

OVERFLOW

Answer

1994

Answer

1000

Question 40

Riley invested $1,000 in savings bonds. If the bonds earn 6.75% interest compounded semi-annually, how much total will Riley earn in 15 years?

Accepted Answer

$2,706.86

Answer

$1,584.62

Answer

$2,651.39

Answer

$1,825.10

Question 41

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.

Accepted Answer

$15,683.28

Answer

$15,415.94

Answer

$15,927.56

Answer

$16,109.05

Question 42

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

Accepted Answer

$2,225.54

Answer

$1,225,54

Answer

$22,255.40

Answer

$225.54

Question 43

The poplulation of Eden is growing continuously at a rate of 1.9%. If the current population is 15,230, about how many years to reach 20,000?

Accepted Answer

15

Answer

31

Answer

2

Answer

68

Question 44

Which of these circumstances would require the formula A=Pe^rt ?

Accepted Answer

Continuously

Answer

Daily

Answer

Monthly

Answer

Quarterly

Question 45

Chelsea put $7500 into an account paying 5% compounded continuously. She now has $10,643.01. How long has the money been in the account?

Accepted Answer

7 years

Answer

6 years

Answer

5 years

Answer

4 years

Question 46

How long will it take $3000 to double if it is invested in an account that pays 3% compounded continuously?

Accepted Answer

23.1 years

Answer

22.1 years

Answer

21.1 years

Answer

20.1 years

Question 47

Write an equivalent equation in logarithmic form: $$10^0$$ = ___.

Accepted Answer

$$\log_{10}1=0$$

Answer

$$\log_110$$ =0

Answer

$$\log_{10}1=10$$

Answer

$$\log_{10}10=1$$

Question 48

log ₉ 27 =

Accepted Answer

3/2

Answer

3

Answer

2/3

Answer

1/3

Question 49

log (1/10,000)

Accepted Answer

-4

Answer

1/4

Answer

1000

Answer

-1000

Question 50

log ₂₅(1/125)

Accepted Answer

-3/2

Answer

-1/5

Answer

5

Answer

2/3

Question 51

log ₃₂ 4 =

Accepted Answer

2/5

Answer

1/8

Answer

8

Answer

5/2

Question 52

log ₁₇ 1

Accepted Answer

0

Answer

1

Answer

17

Answer

18

Unit 9 Retake Exponential and Logarithmic Functions

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