Download Section 3.2 Version 1 - Columbus State University

Section 3.2 Version 1
1. Suppose f is a linear function such that f (–6) = –4 and f (–5) = 4. What is the slope
of f ?
A) –0.10
B) –10.00
C) –8.00
D) 8.00
E) 0.22
2. Suppose f is a linear function such that f (8) = –3 and f (–7) = –6. Find the equation
of f .
A) f = –5.00 x + 37.00
B) f = 5.00 x + 29.00
C) f = –0.20 x – 1.40
D) f = –11.00 x – 83.00
E) f = 0.20 x – 4.60
3. Suppose y is a linear function of x. Decreasing x by 1.8 units causes an increase in y of
2.9 units. What is the slope? Round your answer to two decimal places.
A) 1.61
B) –0.62
C) 0.62
D) –1.61
E) –0.97
4. An elementary school is taking a busload of children to a science fair. It costs $100.00
to drive the bus to the fair and back, and the school pays each student's $3.50 admission
fee. From the formula that expresses the total cost C , in dollars, of the science fair trip
as a linear function of the number n of children who make the trip, calculate the value
of C (3).
A) $303.50
B) $103.50
C) $89.50
D) $310.50
E) $110.50
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5. The total cost C for a manufacturer during a given time period is a function of the
number N of items produced during that period. To determine a formula for the total
cost, we need to know two things. The first is the manufacturer's fixed cost. This amount
covers expenses such as plant maintenance and insurance, and it is the same no matter
how many items are produced. The second thing we need to know is the cost for each
unit produced, which is called the variable cost. Suppose that a manufacturer of widgets
has fixed costs of $1500 per month and that the variable costs are $20 per widget (so it
costs $20 to produce 1 widget). Find the function giving the total monthly cost C , in
dollars, of this widget manufacturer in terms of the number N of widgets produced in a
month.
A) C = 20 N – 1500
B) C = –20 N – 1500
C) C = –1500 N – 20
D) C = 1500 N – 20
E) C = 20 N +1500
6. Suppose that a manufacturer has a total cost of $4700 when 100 widgets are produced
in a month and a total cost of $5600 when 130 widgets are produced in a month. What
are the fixed costs for this manufacturer?
A) $2300
B) $2000
C) $1700
D) $1800
E) $2200
7. Suppose that a manufacturer has a total cost of $6100 when 170 widgets are produced
in a month and a total cost of $6700 when 190 widgets are produced in a month. What
are the variable costs for this manufacturer?
A) $45
B) $30
C) $35
D) $40
E) $15
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8. Suppose that a manufacturer has a fixed cost of $1800 per month and a variable cost of
$35 per widget. Suppose the manufacturer sells 160 widgets for $9600 total. Use a
formula to express the total monthly profit P, in dollars, of this manufacturer as a
function of the number N of widgets produced in a month.
A) P = 35N – 1800
B) P = 25 N
C) P = 25N +1800
D) P = 35 N
E) P = 25N – 1800
9. A real estate agency has fixed monthly costs associated with rent, staff salaries, utilities,
and supplies. It earns its money by taking a percentage commission on total real estate
sales. During the month of July, the agency had total sales of $255,000 and showed a
net income (after paying fixed costs) of $7005. In August total sales were $336,000
with a net income of $11,136. Plot the graph of net income I , in dollars, as a function
of total sales S , in dollars. Let the units on the I axis represent $10,000 and the S axis
represent $100,000.
A)
B)
C)
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D)
E)
10. A real estate agency has fixed monthly costs associated with rent, staff salaries, utilities,
and supplies. It earns its money by taking a percentage commission on total real estate
sales. During the month of July, the agency had total sales of $514,000 and showed a
net income (after paying fixed costs) of $11,788. In August total sales were $755,000
with a net income of $21,910. What are the real estate agency's fixed monthly costs?
A) –$21,588
B) $21,588
C) –$9800
D) $31,710
E) $9800
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11. A real estate agency has fixed monthly costs associated with rent, staff salaries, utilities,
and supplies. It earns its money by taking a percentage commission on total real estate
sales. During the month of July, the agency had total sales of $812,000 and showed a
net income (after paying fixed costs) of $16,704. In August total sales were $266,000
with a net income of only $433. Find the horizontal intercept and explain what this
number means to the real estate agency. Round your answer to the nearest dollar.
A) The horizontal intercept is about $251,470 is the total monthly sales needed for the
agency to break even.
B) The horizontal intercept is about $280,530 is the total monthly sales needed for the
agency to break even.
C) The horizontal intercept is $251,470 and the net income for the agency when there
are no sales.
D) The horizontal intercept is $280,530 and the net income for the agency when there
are no sales.
E) The horizontal intercept is $797,470 and the net profit of the agency for January.
12. Here is a rule of thumb relating yearly income to years spent in secondary education
among adults in their late 20s: If an adult in their late 20s spends 1 year in secondary
education longer than another, then we expect him or her to make an additional yearly
income of $8000. Another related rule of thumb is that a typical adult in their late 20s
who has had 5 years of secondary education will make a yearly income of $55, 200. On
the basis of these two rules of thumb, use a formula to express the trend giving yearly
income I as a linear function of years in secondary education t.
A) Y = –15, 200t – 8000
B) Y = 8000t +15, 200
C) Y = –8000t – 15, 200
D) Y = –8000t +15, 200
E) Y = –15, 200t + 8000
13. Your family likes to eat fruit, but because of budget constraints, you spend only $6 each
week on fruit. Your two choices are apples and grapes. Apples cost $0.60 per pound,
and grapes cost $0.90 per pound. Let a denote the number of pounds of apples you buy
and g the number of pounds of grapes. Because of your budget, it is possible to express
g as a linear function of the variable a. To find the linear formula, we need to find its
slope and initial value. If you buy one more pound of apples, how much less money do
you have available to spend on grapes? Round your answer to the nearest cent.
A) $0.85
B) $0.90
C) $0.60
D) $0.10
E) $0.40
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14. Your family likes to eat fruit, but because of budget constraints, you spend only $6 each
week on fruit. Your two choices are apples and grapes. Apples cost $0.60 per pound,
and grapes cost $0.60 per pound. Let a denote the number of pounds of apples you buy
and g the number of pounds of grapes. Because of your budget, it is possible to express
g as a linear function of the variable a. To find the linear formula, we need to find its
slope and initial value. If you buy one more pound of apples, how many fewer pounds
of grapes can you buy?
A) half pound
B) two pounds
C) one fourth pound
D) three pounds
E) one pound
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Answer Key
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
D
E
D
E
E
C
B
E
C
E
A
B
C
E
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