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Chapter 4: Exponential, Log and Natural Log Functions

Total questions: 45

Worksheet time: 3hrs 11mins

Name
Class
Date
1.
Is the pictured graph growth, decay, or linear or none?  
a)
Growth
b)
Decay
c)
Linear
d)
None
2.

Is the following function and example of decay or growth?

f(x)=2(0.85)x

a)

Exponential Decay

b)

Exponential Growth

3.
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
4.
A population of 1500 deer decreases by 1.5% per year. At the end of 10 years, there will be approximately 1290 deer in the population. Which function can be used to determine the number of deer, y, in this population at the end of t years?
a)
y = 1500(1 - 0.015)t
b)
y = 1500(0.015)t
c)
y = 1500(1 + 0.015)t
d)
y = 1500(1.5)t
5.

Daniel’s Print Shop purchased a new printer for $35,000. Each year it depreciates at a rate of 5%. How much will the printer be worth in 8 years?

a)

$23,219.72

b)

$136.72

c)

$51,710.94

d)

$16,710.94

6.
Twenty years ago, Mr. Davis purchased his home for $160,000. Since then, the value of the home has increased about 5% per year. How much is the home worth today?
a)
$176,783.29
b)
$424,527.63
c)
$57,357.75
d)
$532,041,076.80
7.
Bruno was given $2000 when he turned 3 years old.  His parents invested it at a 2% interest rate compounded annually.  No deposits or withdrawls were made.  Which expression can be used to determine how much money Bruno had in the account when he turned 16? 
a)
2000(1+0.02)13
b)
2000(1-0.02)13
c)
2000(1+0.02)16
d)
2000(1-0.02)16
8.
Karla invested $1,000 in savings bonds. If the bonds earn 6.75% interest compounded semi-annually, how much total will Karla earn in 15 years?
a)
$1,584.62
b)
$2,651.39
c)
$2,706.86
d)
$1,825.10
9.
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
10.

How long will it take for the value of an initial investment of $1200 compounded continuously at a 5.6% interest rate to reach $2000.

a)

9.57 years

b)

9.04 years

c)

9.12 years

d)

.091 years

11.
If $1,000 is invested at 16% interest, compounded continuously, for five years, what is the ending balance?
a)
$1,225,54
b)
$2,225.54
c)
$22,255.40
d)
$225.54
12.
Evaluate log41
a)
1
b)
0
c)
4
d)
undefined
13.
Change to Exponential Form:
log636 = 2
a)
26=36
b)
62=36
c)
362=6
d)
366=2
14.
Solve for x:  log6x + log6(x-5) = 2
a)
√7
b)
9
c)
4
d)
none of these
15.
Solve for x.
ex+6 + 5 = 1
a)
-4.614
b)
-4.236
c)
No Solution
d)
-0.334
16.
Solve the following equation:
4 + 3 log (2x) = 16
a)
x = 3000
b)
x = 0
c)
x = 5000
d)
x = 1,000,000
17.
Find the inverse of f(x) = -4x - 12
a)
f-1(x) = 4x - 3
b)
f-1(x) = -1/4x - 3
c)
f-1(x) = 1/4x + 3
d)
f-1(x) = -4x - 3
18.
The inverse has been reflected over which line?
a)
y = -x
b)
y =x
c)
y = 0
d)
y = x + 1
19.
Use multiple log properties to write as a single log:
log2x -  5log2y
a)
log2(x/y5)
b)
log2(xy5)
c)
log2(x/y)5
d)
log2(x/5y)
20.
Solve:  7ⁿ⁺¹⁰−8 = 6
a)
-7.374
b)
-7.360
c)
-8.644
d)
-8.853
21.

Which function best describes the following graph?

a)

y = Log2 X

b)

2x = y

c)

y = 1/(2x)

d)

(1/2)x = y

22.

How would you describe the range of


Log2 x = y

a)

All Real Numbers

b)

x > 0

c)

y > 0

d)

VA @ x = 0

23.

Solve for X:


Log3 (3x + 4) = Log3 (9x - 40)

a)

X = 6

b)

X = 3

c)

X = 36

d)

X = 9

24.

Write the logarithmic equation in exponential form.
 −2≈ln⁡(0.135)-2\approx\ln\left(0.135\right)  

a)

 −20.135=e-2^{0.135}=e  

b)

 e−2=0.135e^{-2}=0.135  

c)

 e0.135=−2e^{0.135}=-2  

d)

 −2e=0.135-2^e=0.135  

25.
Solve the exponential equation algebraically. (Round to three decimal places)
14e3x+2=560
a)
0.563
b)
3.689
c)
1.442
d)
1.896
26.

Evaluate: ln e2x

a)

e

b)

ln x

c)

2x

d)

2

27.

Convert to exponential form then use a calculator to evaluate ln x = 2

a)

0.6931

b)

0.2010

c)

0.3466

d)

7.3891

28.
Logarithmic functions are the inverse of...
a)
Linear Functions
b)
Exponential Functions 
c)
Quadratic Functions 
d)
Polynomial Functions 
29.
Write the following equation in logarithmic form:
e3 ≈ 20.09
a)
ln3 ≈ 20.09
b)
ln20.09 ≈ 3
c)
lne ≈ 3
d)
ln20.09 ≈ e
30.
f(x) = ∛x is the inverse of which function?
a)
Square root function
b)
Quadratic function
c)
Cubic function
d)
Exponential Function
31.
Evaluate.
3 log24
a)
3
b)
6
c)
2
d)
4
32.

Evaluate the following logarithm:


log42

a)

-1/2

b)

-2

c)

2

d)

1/2

33.
Rewrite in exponential form:
ln(2) = x
a)
2x = 10
b)
102 = x
c)
ex = 2
d)
e2 = x
34.

Evaluate:  5log⁡5255^{\log_525}  

a)

25

b)

2

c)

 5\sqrt{5}  

d)

10

35.
Sovle for x:
5-3x - 1 = 25
a)
x = -1
b)
x = -4
c)
x = -3
d)
x = 1
36.
813-x = (1/3)5x-6
a)
6
b)
-6
c)
9/2
d)
3/2
37.
a)
5
b)
13
c)
84
d)
-20
38.

What is the value of x?

a)

2

b)

1/3

c)

1/35

d)

-1/35

39.
Solve the equation for x.
a)
32
b)
25
c)
1.66
d)
512
40.
log2(x + 2) + log2x  = 3
a)
-4, 2
b)
-2, 4
c)
2
d)
1
41.
Solve.
e4x=12
a)
2.48
b)
9.94
c)
0.62
d)
3
42.
Solve the following equation.  Round your answer to two decimal places;
5 ln(x) = 7
a)
x = 4.06
b)
x = 2.04
c)
No solution
d)
None of the above
43.
a)
(2e+2)/3
b)
0
c)
(2e-2)/3
d)
(3e-2)/2
44.

log8(4x+4)=2

a)

15

b)

12

c)

10

d)

3

45.

Solve 3e5x - 6 = 24 to 3 decimal places.

a)

0.227

b)

2.303

c)

0.736

d)

0.461

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