Modeling with Mathematics: A Bridge to Algebra II
Form A
Chapter 6 Assessment
1
Which of the following is not a representation of exponential growth?
A
C
B
2
x
y
0
1
1
3
2
9
3
27
x
y
0
1
1
1.5
2
2.25
3
3.375
D
Which of the following equations is
a correct representation of
y = log10 x ?
A x = log10 y
B
y = 10 x
C
x = 10
3
There were about 6 billion humans
on Earth in the year 2000. If human
beings double their population
every 50 years, what will be the
human population in the year 2500?
A 6,144,000,000,000
B 6,144,000,000
y
D x = 10 ( log y )
C 614,400,000,000
D 61,440,000,000
© 2006 Region 4 Education Service Center. All rights reserved.
Use authorized only for the district participating in this pilot project.
Page 1 of 7
Modeling with Mathematics: A Bridge to Algebra II
Form A
Chapter 6 Assessment
4
The table shows the amount of a
medication in a tiger’s blood stream
over a period of time.
Time
(hours)
6
A The speed of a car traveling at a
constant rate as it gets closer to
home
Amount of
Medication
(milligrams)
350
262.5
196.88
147.66
110.74
83.057
0
1
2
3
4
5
B The number of milligrams of a
cold medication in your blood
stream if your body eliminates
one half of the medication every
hour
C The number of weeds in a
garden if every weed reproduces
exactly 1 new weed in its
lifetime
Which function rule best models the
relationship between the number of
hours, h, and the number of
milligrams of medication remaining
in the tiger’s blood stream, M?
D The height of a ball over time
when it is dropped from a
building
A M = 12.5h + 350
B
M = 0.75h
C M = 0.75h + 350
D M = 350 ( 0.75 )
5
Which of the following situations
would best be modeled by an
exponential decay function?
h
The half-life of a radioactive
substance is the amount of time
required for half of a given sample
to decay. A container holds 1000
grams of a certain substance that
has a half-life of one year.
Approximately how many grams of
the substance will remain in the
container after 10 years?
A 0.244 grams
B 0.5 grams
7
The amount of air remaining in an
inflated balloon can be modeled by
d
the function V = 2000 ( 0.85 )
where d represents the number days
after inflation and V represents the
volume of the balloon in milliliters
(mL).
What will be the approximate
volume of air in the balloon after 10
days?
A 0.394 mL
B 3.94 mL
C 394 mL
D
1700 mL
C 0.977 grams
D 100 grams
© 2006 Region 4 Education Service Center. All rights reserved.
Use authorized only for the district participating in this pilot project.
Page 2 of 7
Modeling with Mathematics: A Bridge to Algebra II
Form A
Chapter 6 Assessment
8
When a sheet of paper is cut in half, then the half is cut in half and so on, the area of the of the
region remaining can be modeled using an exponential decay function. Which of the
following tables shows an example of exponential decay?
A
B
x
y
0
C
x
y
0
0
1
1
-2
1
1.5
2
-8
2
2.25
3
-18
3
3.375
4
-32
4
5.0625
x
y
x
y
0
-5
0
1
1
-7
1
0.75
2
-9
2
0.5625
3
-11
3
0.421875
4
-13
4
0.3160625
D
© 2006 Region 4 Education Service Center. All rights reserved.
Use authorized only for the district participating in this pilot project.
Page 3 of 7
Modeling with Mathematics: A Bridge to Algebra II
Form A
Chapter 6 Assessment
9
The table shows the population
growth of one Knapweed plant over
a 5-year period.
Time
(years)
0
1
2
3
4
5
11
The table represents a transformation
of the function y = 5 x .
Number of
Plants
1
12
144
1728
20736
248832
x
0
y
6
1
10
2
30
3
130
4
630
Which function rule models the
transformed data?
Which function rule best models the
relationship between the number of
years, x, and the number of
Knapweed plants produced, y?
10
A
y = 11.92 x
B
y = 12 x
C
y = 12 x 2
D
y = 12 × 2 x
Cell growth can be modeled using
the function y = 2 x where x
represents the number of times the
cell doubles and y represents the
number of cells after each doubling.
What will be the number of cells
present after a cell doubles 14
times?
A 28
B 196
C 4096
D 16384
12
A
y = 6(5) x
B
y = 5x + 5
C
y = 2(5) x
D
y = 5x + 6
Which of the following situations
would best be modeled by an
exponential growth function?
A Height of a diver above the
ground over time when they
jump off a high dive into a
swimming pool
B Amount of money in your piggy
bank if you add $0.25 every day
C Total number of plants in a
greenhouse if each plant
produces 2 new plants every 5
days
D Population growth if every
couple has two children or less
during their lifetime
© 2006 Region 4 Education Service Center. All rights reserved.
Use authorized only for the district participating in this pilot project.
Page 4 of 7
Modeling with Mathematics: A Bridge to Algebra II
Form A
Chapter 6 Assessment
13
If rabbits are allowed to reproduce without restriction, the population will experience
exponential growth. Which of the following tables shows an example of exponential growth?
A
B
x
y
0
C
x
y
5
0
5
1
25
1
7
2
125
2
13
3
625
3
23
4
3125
4
37
x
y
x
y
0
5
0
5
1
7
1
1
2
9
2
0.2
3
11
3
0.04
4
13
4
0.008
D
© 2006 Region 4 Education Service Center. All rights reserved.
Use authorized only for the district participating in this pilot project.
Page 5 of 7
Modeling with Mathematics: A Bridge to Algebra II
14
Form A
Chapter 6 Assessment
Which of the following is a representation of exponential decay?
A
C
B
15
D
x
y
x
y
0
0
0
1
1
-2
1
0.8
2
-8
2
0.6
3
-18
3
0.4
Which of the following expressions
is equivalent to log 2 75 + log 2 3 ?
16
Which of the following will yield a
vertical compression of the graph of
the function y = 0.75 x ?
A log 2 25
A
y = 0.75 x + 2
B
y = 0.75 x − 4
C
y = 0.2(0.75) x
D
y = 5(0.75) x
B log 2 225
C log 4 78
D log 2 78
© 2006 Region 4 Education Service Center. All rights reserved.
Use authorized only for the district participating in this pilot project.
Page 6 of 7
Modeling with Mathematics: A Bridge to Algebra II
Form A
Chapter 6 Assessment
17
A scientist in a recent science fiction movie stated that if a killer bacterium were allowed to
grow uncontrolled, its mass would be greater than the Earth’s mass in less than one week.
The bacterium doubles its mass every hour, and the mass of one bacterium is 10−12 grams.
Given that the mass of the Earth is about 5.98 ×1027 grams, is the statement reasonable?
Justify your answer.
© 2006 Region 4 Education Service Center. All rights reserved.
Use authorized only for the district participating in this pilot project.
Page 7 of 7