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Assessment Review Exponential & Logarithm

Total questions: 61

Worksheet time: 2hrs 2mins

Name
Class
Date
1.
Rewrite 34 = 81 in logarithmic form.
a)
log34 = 81
b)
log813 = 4
c)
log381 = 4
d)
log481 = 3
2.
Change to Exponential Form:
log636 = 2
a)
26=36
b)
62=36
c)
362=6
d)
366=2
3.
Evaluate. 
a)
A
b)
B
c)
C
d)
D
4.
Evaluate:
log416
a)
2
b)
4
c)
1/2
d)
-2
5.
Rewrite log28 = 3 in exponential form/
a)
28 = 3
b)
23 = 8
c)
32 = 8
d)
83 = 2
6.
log525 = ?
a)
2
b)
5
c)
125
7.
Write in exponential form.
log2(1/8) = -3
a)
2-3 = 1/8
b)
21/8 = -3
c)
-32 = 1/8
d)
-31/8 = 2
8.
Change to Exponential Form:
log636 = 2
a)
26=36
b)
62=36
c)
362=6
d)
366=2
9.
Evaluate the following logarithm by converting to exponential form.
log3⅓ = x
a)
x = -1
b)
x = 1
c)
x = 3
d)
x = ⅓
10.
Is the pictured graph growth, decay, or linear or none?  
a)
Exponential Growth
b)
Exponential Decay
c)
Linear
d)
None
11.
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
12.

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

a)

Slope

b)

Rate of change

c)

Y-intercept

d)

Multiplier

13.
Which of the following is an increasing exponential function whose y-intercept is 50?
a)
y = 50(.05)x
b)
y = 50x - 4
c)
y = (2)x + 50
d)
y = 50(1.4)x
14.
The amount of ants in a colony, f, that is decaying can be modeled by                      f(x) = 800(.87)x, where x is the number of days since the decay started. By what percentage is the colony decaying?
a)
87%
b)
13%
c)
800%
d)
8.7%
15.
A collectible car has been going up in price by 10% each year. If the car is already worth $29,000, how much will the car be worth in 5 years?
a)
$0.29
b)
$2,900,000,000
c)
$46,704.79
d)
$145,000
16.
The amount of ibuprofen (medicine for headaches) breaks down by 30% each hour. If a person took a 200 milligram ibuprofen, how much will be left after 3 hours?
a)
5.4 mg
b)
68.6 mg
c)
.0054 mg
d)
2,400,000 mg
17.
Rewrite 34 = 81 in logarithmic form.
a)
log34 = 81
b)
log813 = 4
c)
log381 = 4
d)
log481 = 3
18.
Rewrite log28 = 3 in exponential form.
a)
28 = 3
b)
23 = 8
c)
32 = 8
d)
83 = 2
19.
Evaluate:
log416
a)
2
b)
4
c)
1/2
d)
-2
20.
Change to Exponential Form:
log636 = 2
a)
26=36
b)
62=36
c)
362=6
d)
366=2
21.
Classify the given graph.
a)
exponential growth
b)
exponential decay
c)
positive linear
d)
negative linear
22.

Evaluate.

a)
A
b)
B
c)
C
d)
D
23.

Evaluate.

a)
A
b)
B
c)
C
d)
D
24.
Rewrite the equation in logarithmic form.
a)
A
b)
B
c)
C
d)
D
25.
Logarithmic functions are the inverse of...
a)
Linear Functions
b)
Exponential Functions 
c)
Quadratic Functions 
d)
Polynomial Functions 
26.
Change to Exponential Form:
log636 = 2
a)
26=36
b)
62=36
c)
362=6
d)
366=2
27.
What is the End behavior on the right side
a)
 x→∞, y→∞
b)
 x→⁻∞, y→∞
c)
 x→⁻∞, y→0
d)
 x→∞, y→⁻∞
28.
What is the End behavior on the left side
a)
 x→∞, y→∞
b)
 x→⁻∞, y→∞
c)
 x→⁻∞, y→0
d)
 x→∞, y→⁻∞
29.
What is the end behavior of the function
a)
 x →∞, y→⁻∞ and x →⁻∞,y→⁻∞
b)
x →∞, y→∞ and x→⁻∞, y→∞
c)
x →∞, y→∞ and x→⁻∞, y→2
d)
 x →∞,y→2 and x→⁻∞, y→∞
30.
Which one means the function goes up on the left
a)
x →-∞, y→∞
b)
x →-∞, y→-∞
31.
Which one means up
a)
y →-∞
b)
y →∞
32.

What is the y-intercept of the function?

a)

1

b)

2

c)

4

d)

3

33.

Write an equation that models the following situation:

The current student count at John Jay is 6500, it is expected to grow at a rate of 14% next year.

a)

y= 6500(1+.14)x

b)

y= 6500(1-.14)x

c)

y= 6500(14)x

d)

y= 14(6500)x

34.

What type of function is y=7(5)x

a)

Exponential Growth

b)

Linear Function

c)

Exponential Decay

d)

Quadratic Function

35.

Which of the followings functions shows an initial amout of $15 and an increase of 35% ?

a)

y=15(35)x

b)

y=15(1.35)x

c)

y=15(0.35)x

d)

y=35(15)x

36.

What is the y-intercept of the function f(x)=2(4)x ?

a)

2

b)

4

c)

(4)x

d)

8

37.

What is the exponential factor of the following graph?

a)

Growth

b)

Deccay

c)

Linear

d)

None

38.

What is the exponential factor of the graph?

a)

Growth

b)

Decay

c)

Linear

d)

None

39.
What is a, the starting term, for the function: f(x) = 300(1.16)x?
a)
300
b)
1.16
c)
.16
d)
x
40.
What does the y-intercept of the graph represent?
a)
The amount of grams the material is gaining.
b)
The amount of grams the material is losing.
c)
The amount of grams remaining after so many years.
d)
The initial amount of grams.
41.
Which of the following is an increasing exponential function whose y-intercept is 50?
a)
y = 50(.05)x
b)
y = 50x - 4
c)
y = (2)x + 50
d)
y = 50(1.4)x
42.
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
43.

Which equation matches this graph?

a)
b)
c)
d)
44.

Which graph matches the equation?

a)
b)
c)
d)
45.

Which graph matches this equation?

a)
b)
c)
d)
46.

Which graph matches this equation?

a)
b)
c)
d)
47.

If g(x) is a transformation of f(x), describe the transformation.

f(x)=2xf\left(x\right)=2^x      g(x)=2x+4g\left(x\right)=2^x+4   

a)

Up 4 units

b)

Down 4 units

c)

Left 4 units

d)

Right 4 units

48.

 If g(x) is a transformation of f(x), describe the transformation.

f(x)=0.4x−1f\left(x\right)=0.4^x-1
g(x)=0.4x−2g\left(x\right)=0.4^x-2  

 

a)

Down 1 unit

b)

Down 2 units

c)

Up 1 unit

d)

Up 2 units

49.

 If g(x) is a transformation of f(x), describe the transformation.

g(x)=0.5x−3g\left(x\right)=0.5^{x-3}   
f(x)=0.5xf\left(x\right)=0.5^x  

a)

Left 3 units

b)

Right 3 units

c)

Up 3 units

d)

Down 3 units

50.

 If f(x) is a transformation of g(x), describe the transformation.

g(x)=0.5x−3g\left(x\right)=0.5^{x-3}   
f(x)=0.5xf\left(x\right)=0.5^x  
Be careful!  Pay attention to the order of the functions.

a)

Left 3 units

b)

Right 3 units

c)

Up 3 units

d)

Down 3 units

51.

Describe the transformation:

f(x)=4x+2−3f\left(x\right)=4^{x+2}-3  

a)

Translate Up 2 and Right 3

b)

Translate Right 2 and Down 3

c)

Translate Left 2 and Down 3

d)

Translate Down 2 and Right 3

52.

What is the y-intercept of the function y=4(5)x?y=4\left(5\right)^x?  

a)

(0, 0)

b)

(0, 4)

c)

(0, 5)

53.

How has the function y=7(3)x−5y=7\left(3\right)^x-5 been transformed from the parent function  y=7(3)xy=7\left(3\right)^x ?

a)

Translated up 5

b)

Translated down 5

c)

Reflection over the x-axis

d)

Reflection over the y-axis

54.
What kind of shift  is represented?
a)
up 1 unit
b)
left 1 unit
c)
right 1 unit 
d)
down 1 unit
55.

How does the graph of g(x) =undefinedcompare to f(x) =undefined

a)

The graph of g(x) is a translation 6 units down from the graph of f(x).

b)

The graph of g(x) is a translation 6 units up from the graph of f(x).

c)

The graph of g(x) is a translation 6 units right from the graph of f(x).

d)

The graph of g(x) is a translation 6 units left from the graph of f(x).

56.

What transformation maps f(x)=2xf\left(x\right)=2^x  to  g(x)=2x−8g\left(x\right)=2^{x-8}  

a)

Translates left 8 units

b)

Translates right 8 units

c)

Translates up 8 units 

d)

Translates down 8 units

57.
An adult takes 400 mg of ibuprofen. Each hour, the amount of ibuprofen in the person’s system decreases by about 29%. How much ibuprofen is left after 6 hours? 
a)
51 mg
b)
284 mg
c)
1843 mg
d)
116 mg
58.
You buy a new computer for $2100. The computer decreases by 50% annually. When will the computer have a value of $600?
a)
between 1 and two years
b)
more than 5 years
c)
less than a year
d)
between 3 and 4 years
59.
You buy a new computer for $2100. The computer decreases by 50% annually. What would be the multiplier for this problem?
a)
1.5
b)
.5
60.
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? 
a)
19 to 20 hours
b)
10 to 20 hours
c)
15 to 16 hours
d)
5 to 6 hours
61.
The foundation of your house has about 1,200 termites. The termites grow at a rate of about 2.4% per day. How long until the number of termites doubles?
a)
29 to 30 years
b)
23 to 24years
c)
15 to 16 years
d)
19 to 20 years

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