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Exponential Functions and Log Properties

Total questions: 39

Worksheet time: 3hrs 44mins

Name
Class
Date
1.
Classify the model as Exponential GROWTH or DECAY.
A=1200(.85)6
a)
Growth
b)
Decay
2.
Classify the model as Exponential GROWTH or DECAY.
A=10(1.01)3
a)
Growth
b)
Decay
3.

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=14(6)x

c)

y=6(1.14)x

d)

y=6(0.86)x

4.
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=5000xx
5.

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?

a)

2036

b)

9006

c)

9765

d)

5433

6.
Is the pictured graph growth, decay, or linear or none?  
a)
Exponential Growth
b)
Exponential Decay
c)
Linear
d)
None
7.

Is this exponential growth or decay?

a)

Growth

b)

Decay

c)

logarithmic

d)

Square Root

8.
The initial deposit or investment is called 
a)
Interest
b)
Principal
c)
Savings
d)
Capital gain
9.
Monthly means how many times a year?
a)
4 
b)
12
c)
52
d)
365
10.
Semi-Annually means how many times a year?
a)
4 
b)
2
c)
1
d)
6
11.
An antibiotic is introduced into a colony of 12,000 bacteria during a laboratory experiment. The colony is decreasing by 14.9% per minute. Which function can be used to model the number of bacteria in the colony after x minutes?
a)
f(x) = 12000(1 + 14.9)x
b)
f(x) = 12000(1 - 14.9)x
c)
f(x) = 12000(1 + 0.149)x
d)
f(x) = 12000(1 - 0.149)x
12.

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

a)

SLOPE

b)

Rate of Growth

c)

Initial Value

d)

Time

13.
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.
a)
$15,415.94
b)
$15,683.28
c)
$15,927.56
d)
$16,109.05
14.
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?
a)
$1,584.62
b)
$2,651.39
c)
$2,706.86
d)
$1,825.10
15.

Mark took a loan out for $25,690 to purchase a truck. At an interest rate of 5.2% compounded monthly, how much total will he have paid after 5 years?

a)

$33,299.42

b)

$33,672.68

c)

$34,157.04

d)

$34,710.88

16.

If $400 is invested at 35% interest, compounded continuously, for 2 years, what is the ending balance?

a)

$280

b)

$680

c)

$1,034.47

d)

$805.50

17.
Evaluate the log:
log3(1/9) = 
a)
1/2
b)
2
c)
-2
d)
3
18.
Rewrite as a single log:
log 5 + log 7
a)
log 12
b)
log -2
c)
log 35
d)
undefined
19.
Write as a single log:
log 12 - log 2
a)
log 6
b)
log 10
c)
0
d)
2
20.
Rewrite using log rules:
log4x2
a)
log4 + logx2
b)
log4/logx2
c)
log4x2
d)
2log4x
21.
Rewrite the equation in exponential form.
a)
24=16
b)
42=16
c)
164=2
d)
416=2
22.
Rewrite the equation in exponential form.
a)
15r=26
b)
26r=15
c)
2615=r
d)
1526=r
23.
Rewrite the equation in logarithmic form.
a)
log17289=2
b)
log2289=17
c)
log172=289
d)
log22=289
24.
Rewrite the equation in logarithmic form.
a)
logb50=a
b)
loga50=b
c)
log50b=a
d)
logab=50
25.
Rewrite the equation in logarithmic form.
a)
logxy=(1/9)
b)
logyx=(1/9)
c)
log(1/9)x=y
d)
logy(1/9)=x
26.
When a logarithm has division inside of it, it expands using ________________.
a)
Addition
b)
Subtraction
c)
Multiplication
d)
Division
27.
Write as a single log: log 12 + 2 log x
a)
log (12 + 2x)
b)
log (14x)
c)
log (12 * 2x)
d)
log (12x2)
28.
Expand.
a)
log x + 5 log y
b)
5 log x + 5 log y
c)
5 log x - log y
d)
log x - 5 log y
29.
Expand.
a)
1/3 log x + log y + log z
b)
1/3 log x + 1/3 log y + 1/3 log z
c)
1/3 log x - 1/3 log y - 1/3 log z
d)
3 log x + 3 log y + 3 log z
30.

Write as a single logarithm.

16 log u +4 log v

a)

log(v4u16)

b)

log(v4u4)

c)

log(vuw4)

31.
Expand log5(u3v5)
a)
1/2(log5u+log5v+log5uw)
b)
5 log5 u - 15 log5 v 
c)
log5u + log5v +3 log5w
d)
3 log5u + 5 log5v
32.

Using the change of base rule, what is log5 83 equivalent to?

a)

3.091

b)

2.365

c)

2.746

d)

1.804

33.

Given log x3 , What is the base of the log?

a)

x

b)

3

c)

0

d)

10

34.

What is the percent of growth or decay?

A=1200(.85)6

a)

85%

b)

15%

c)

1200%

d)

6%

35.

What is the rate of growth written as a percent? y=(3.6)x

a)

3.6%

b)

360%

c)

2.6

d)

260%

36.

What is the initial value? y=(3.6)x

a)

1

b)

3.6

c)

360

d)

3

37.

An investment firm Compounds Continuously on investments. If you invest 40,000 at 1.25% interest, how much will you have after 12 years? Round your answer to the nearest dollar.

a)

46430.00

b)

46473.00

c)

52891.00

d)

75230.00

38.

True or False log66=0

a)

True

b)

False

c)

None of the above:)

39.

Identify the type of function in the graph.

a)

Square root

b)

Exponential Growth

c)

Exponential Decay

d)

Logarithm

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