The number of members f(x) in Joe's health club increased by 25%
every year over a period of x years. The function below shows the
relationship between f(x) and x:
f(x) = 15(1.25)x
Which of
the following graphs best represents the function?
Question 2
(Multiple Choice Worth 1 points)
(04.06)
A store had 175 cell phones in the month of January.
Every month, 10% of the cell phones were sold and 10 new cell
phones were stocked in the store.
Which recursive function
best represents the number of cell phones in the store f(n) after n
months?
f(n) = 175 − 0.9 × f(n − 1) + 10, f(0) = 175, n > 0
f(n) = 0.1 × f(n − 1) + 10, f(0) = 175, n > 0
f(n) = 175 + 0.9 × f(n − 1) + 10, f(0) = 175, n > 0
f(n) = 0.9 × f(n − 1) + 10, f(0) = 175, n > 0
Question 3
(Multiple Choice Worth 1 points)
(04.03)
The graph below shows three functions:
Which function
has all real numbers as its domain?
Only f(x)
Both g(x) and p(x)
Both f(x) and g(x)
Only p(x)
Question 4
(Multiple Choice Worth 1 points)
(04.05)
The average annual salary of the employees of a
company in the year 2005 was $80,000. It increased by the same
factor each year and in 2006, the average annual salary was
$88,000. Let f(x) represent the average annual salary, in thousand
dollars, after x years since 2005. Which of the following best
represents the relationship between x and f(x)?
f(x) = 88(0.88)x
f(x) = 88(1.1)x
f(x) = 80(0.88)x
f(x) = 80(1.1)x
Question 5
(Multiple Choice Worth 1 points)
(04.05)
The number of subscribers y to a newspaper after t
years is shown by the equation below:
y = 75(0.95)t
Which
conclusion is correct about the number of subscribers to the
newspaper?
It increased by 75% every year.
It decreased by 75% every year.
It increased by 5% every year.
It decreased by 5% every year.
Question 6
(Multiple Choice Worth 1 points)
(04.01)
Simplify
Question 7
.
(Multiple Choice Worth 1 points)
(04.02)
What is the exact value of the expression
+
? Simplify if possible.
8
12
8
12
Question 8
(Multiple Choice Worth 1 points)
−
(04.05)
The price of bronze has increased by 10% per year
from 2000. In the year 2000, Harry bought a bronze medal for
$120. Which of the following functions f(x) can be used to
represent the price of the medal x years after 2000?
f(x) = 120(0.9)x
f(x) = 10(120)x
f(x) = 120(1.1)x
f(x) = 10(1.1)x
Question 9
(Multiple Choice Worth 1 points)
(04.03)
Jake forgot to replace the cap on a bottle of cologne.
The cologne began to evaporate at the rate of 18% per day. If the
original amount of cologne in the bottle was 50 grams, which of
the following graphs best represents the amount of cologne f(x)
remaining in the bottle after x days?
Question 10
(Multiple Choice Worth 1 points)
(04.03)
The function f(x) = 800(1.09)4x shows the growth due to
interest that Jim earns on an investment.
The steps to calculate
an equivalent function are shown below:
[Step
f(x) =
1]
800(1.09)4x
[Step
f(x) =
2]
800(1.094)x
[Step
f(x) =
3]
800(1.4116)x
[Step
4]
f(x) = (1129.27)x
Which of the following is the first incorrect step?
Step 1
Step 2
Step 3
Step 4
Question 11
(Multiple Choice Worth 1 points)
(04.07)
The functions f(x) and g(x) are shown below:
f(x) =
0.05x
g(x) = (0.05)x
Which statement best describes the
graph of f(x) and g(x)?
The graph of g(x) will eventually exceed the graph of f(x).
The graph of f(x) will eventually exceed the graph of g(x).
The graphs will both have their y-intercept equal to 1.
The graphs will both have their y-intercept equal to 0.05
Question 12
(Multiple Choice Worth 1 points)
(04.03)
Jack invested some money in a bank at a fixed rate of
interest compounded annually. The equation below shows the
value of his investment after x years:
f(x) = 300(1.02)x
What
was the average rate of change of the value of Jack's investment
from the third year to the fifth year?
6.43 dollars per year
8.24 dollars per year
12.86 dollars per year
14.26 dollars per year
Question 13
(Multiple Choice Worth 1 points)
(04.05)
Which statement best describes the effect of replacing
the function f(x) = 2x + 2 with the function g(x) = 2x − 3?
The graph shifts 1 unit left.
The graph shifts 5 units left.
The graph shifts 5 units right.
The graph shifts 1 unit right.
Question 14
(Multiple Choice Worth 1 points)
(04.03)
The number of users of the internet in a town increased
by a factor of 1.01 every year from 2000 to 2010. The function
below shows the number of internet users f(x) after x years from
the year 2000:
f(x) = 3000(1.01)x
Which of the following is
a reasonable domain for the function?
0 ≤ x ≤ 10
2000 ≤ x ≤ 2010
0 ≤ x ≤ 3000
All positive integers
Question 15
(Multiple Choice Worth 1 points)
(04.03)
Which of the following is an equivalent function to the
function below?
f(x) = 50(1.05)12x
f(x) = 50(1.7959)x
f(x) = 50(12.6000)x
f(x) = 600(1.05)x
f(x) = 4.2(1.05)x
Question 16
(Multiple Choice Worth 1 points)
(04.06)
Bruce added some chlorine to the water in a pool. The
chlorine evaporated at a fixed rate every week. The table below
shows the amount of chlorine f(n), in ounces, that was left in the
pool after n weeks:
n
f(
n)
1 54
2 27
3
4
13
.5
6.
75
Which function best shows the relationship between n and f(n)?
f(n) = 108(0.5)n− 1
f(n) = 54(0.5)n
f(n) = 108(0.5)n+1
f(n) = 54(0.5)n− 1
Question 17
(Multiple Choice Worth 1 points)
(04.03)
A dance competition on television had five elimination
rounds. After each elimination, only one-fourth of the contestants
were sent to the next round. The table below shows the number of
contestants in each round of the competition:
x 1
f
(
x
)
2
5
1
1
2
2
8
3 45
3
2
82
Compute the average rate of change of f(x) from x = 2 to x = 4
and describe what it represents.
− 60 contestants per round, and it represents the average rate at
which the number of contestants changed from the second round
to the fourth round
− 120 contestants per round, and it represents the average rate at
which the number of contestants changed from the second round
to the fourth round
− 60 contestants per round, and it represents the number of
contestants who will reach the final round
− 120 contestants per round, and it represents the number of
contestants who will reach the final round
Question 18
(Multiple Choice Worth 1 points)
(04.02)
An expression is shown below:
Which statement is true about the expression?
It is rational and equal to 3.
It is rational and equal to 4.
It is irrational and equal to
.
It is irrational and equal to
.
Question 19
(Multiple Choice Worth 1 points)
(04.05)
The graphs below show four functions:
Which graph
best shows the function f(x) = 3(3)− x to represent the rate at
which a radioactive substance decays?
Graph A
Graph B
Graph C
Graph D
Question 20
(Multiple Choice Worth 1 points)
(04.05)
The table below shows the functions to represent the
sale f(t), in thousands, of four companies in t years:
Compa
ny
Sale
A
B
C
D
f(t) =
f(t) =
f(t) =
f(t) =
1.05t
0.75t
1.212t
0.9712t
Which of the following companies showed an exponential decay in
sale?
Company A and Company C
Company B and Company D
Company C and Company D
Company A and Company B
Question 21
(Multiple Choice Worth 1 points)
(04.01)
Which of the following is equal to
?
Question 22
(Multiple Choice Worth 1 points)
(04.01)
Which of the following best defines
?
Cube root of 4
Square root of 4
Cube root of 2
Square root of 2
Question 23
(Multiple Choice Worth 1 points)
(04.06)
The sales totals at Linda's food store have increased
exponentially over the months. Which of these best shows the
sales in the first three months?
$1200 in the first month, $1260 in the second month, and $1323
in the third month
$1200 in the first month, $1250 in the second month, $1300 in the
third month
$1200 in the first month, $1272 in the second month, $1344 in the
third month
$1200 in the first month, $1285 in the second month, $1370 in the
third month
Question 24
(Multiple Choice Worth 1 points)
(04.03)
Jane is studying the rate at which the sale of a
particular brand of chocolate has increased over the years. The
graph below shows the number of bars sold y, in thousands, after
x years since the year 2000:
What does the
y-intercept of the graph represent?
Price of a bar of chocolate
Number of bars sold in 2000
Number of bars sold before 2000
Rate of increase in the sale of chocolates
Question 25
(Multiple Choice Worth 1 points)
(04.07)
The functions f(x) and g(x) in the table below show
Kim's and Ben's savings respectively, in dollars, after x days. Some
values are missing in the table.
x(years)
12 3
g(x) = 3x
Kim's savings in
39
dollars
f(x) = 3x + 5
Ben's savings in
dollars
8
1
1
Which statement best describes Kim and Ben's savings in the long
run?
The savings will increase by the same factor for both.
The savings will increase by the same amount for both.
Kim will save more than Ben.
Ben will save more than Kim.
Question 26
(Multiple Choice Worth 1 points)
(04.01)
Which of the following shows the correct steps to find
the value of
?
Question 27
(Multiple Choice Worth 1 points)
(04.07)
The same amount of trash from a landfill is recycled
every day. The function below shows the total number of tons of
trash n left in the landfill after x days. Assume that new trash is not
added to the landfill.
n = 50000 − 1000x
What does the
number 1000 represent?
Amount of trash left after 1 day
Amount of trash recycled in x days
Amount of trash recycled every day
Amount of trash originally in the landfill
Question 28
(Multiple Choice Worth 1 points)
(04.05)
The population f(x), in millions, of State A of a country
after x years is represented by the function shown below:
f(x) =
4(1.08)x
The graph shows the population g(x), in millions, of
State B of the country after x years:
Which
conclusion is correct about the population of State A and State B?
The original population of State A was double of the original
population of State B.
The original population of State B was double of the original
population of State A.
The original population of State A was four times of the original
population of State B.
The original population of State A was equal to the original
population of State B.
Question 29
(Multiple Choice Worth 1 points)
(04.07)
A ball is dropped from a certain height. The function
below represents the height f(n), in feet, to which the ball bounces
at the nth bounce:
f(n) = 9(0.7)n
What does the number 9
in the function represent?
Number of times the ball was dropped.
Height from which the ball was dropped.
Height to which the ball will bounce at the nth bounce.
Number of times the ball bounces at the nth bounce.
Question 30
(Multiple Choice Worth 1 points)
(04.06)
Scott and Harry went cycling every day. They increased
the number of minutes of cycling every week as described
below:
Scott: Cycled for 10 minutes every day in the first week,
15 minutes in the second week, 20 minutes in the third week, and
25 minutes in the fourth week.
Harry: Cycled for 10 minutes
every day in the first week, 20 minutes in the second week, 40
minutes in the third week, and 80 minutes in the fourth
week.
Which statement best describes the methods used by
Scott and Harry to increase the time they spent cycling?
Scott's method is linear because the number of minutes increased
by an equal number every week.
Harry's method is linear because the number of minutes increased
by an equal factor every week.
Both Harry's and Scott's method is exponential because the
number of minutes increased by an equal factor every week.
Both Harry's and Scott's method is exponential because the
number of minutes increased by an equal number every week.
Question 31
(Multiple Choice Worth 1 points)
(04.07)
The amount of a radioactive material changes with
time. The table below shows the amount of radioactive material f(t)
left after time t:
t(hou
rs)
0
1
f(t)
0
0
1 2
5 2
0 5
Which exponential function best represents the relationship
between f(t) and t?
f(t) = 0.5(100)t
f(t) = 100 (0.25)t
f(t) = 0.25(50)t
f(t) = 100(0.5)t
Question 32
(Multiple Choice Worth 1 points)
(04.05)
Maureen is taking an antibiotic. The table below shows
the amount of antibiotic f(t), in mg, that was present in her body
after time t:
t
(hours 1
2 3 4
5
)
f(t)
(mg)
1
5
0
9 5 32 19
0 4 .4
.4
Ken was administered 200 mg of the same antibiotic. The amount
of antibiotic f(t) in his body after time t is shown by the equation
below:
f(t) = 200(0.976)t
Which statement best describes the rate at which Maureen's and
Ken's bodies eliminated the antibiotic?
Maureen's body eliminated the antibiotic faster than Ken's body.
Maureen's body eliminated the antibiotic at the same rate as Ken's
body.
Maureen's body eliminated the antibiotic at half of the rate at
which Ken's body eliminated the antibiotic.
Maureen's body eliminated the antibiotic at one-fourth of the rate
at which Ken's body eliminated the antibiotic.
Question 33
(Multiple Choice Worth 1 points)
(04.05)
The graph of f(x) = 2x + 4 shifts six units to the right
when it is replaced with the graph of f(x) = 2x − k. What is the
value of k?
2
4
6
10