Section 3.2 Version 2

Transcription

1 Section 3.2 Version 2 1. Suppose f is a linear function such that f (1) = 1 and f ( 7) = 3. What is the slope of f? A) 0.33 B) 2.00 C) 2.00 D) 0.50 E) Suppose f is a linear function such that f (1) = 8 and f ( 1) = 6. Find the equation of f. A) f = 0.71 x B) f = 1.40 x C) f = 0.14 x D) f = 1.40 x E) f = 7.00 x Suppose y is a linear function of x. Decreasing x by 4.2 units causes an increase in y of 6.2 units. What is the slope? Round your answer to two decimal places. A) 1.48 B) 0.68 C) 0.68 D) 1.48 E) An elementary school is taking a busload of children to a science fair. It costs $ to drive the bus to the fair and back, and the school pays each student's $3.00 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 (7). A) $ B) $ C) $ D) $ E) $ Version 2 Page 1

2 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 $1200 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 1200 B) C = 20 N C) C = 1200 N 20 D) C = 1200 N + 20 E) C = 20 N Suppose that a manufacturer has a total cost of $6100 when 110 widgets are produced in a month and a total cost of $8500 when 170 widgets are produced in a month. What are the fixed costs for this manufacturer? A) $1300 B) $1200 C) $1700 D) $1600 E) $ Suppose that a manufacturer has a total cost of $4300 when 80 widgets are produced in a month and a total cost of $6100 when 140 widgets are produced in a month. What are the variable costs for this manufacturer? A) $20 B) $30 C) $45 D) $15 E) $40 Version 2 Page 2

3 8. Suppose that a manufacturer has a fixed cost of $1300 per month and a variable cost of $30 per widget. Suppose the manufacturer sells 110 widgets for $4950 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 = 15N B) P = 30 N 1300 C) P = 45N D) P = 45 N 1300 E) P = 15 N 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 $290,000 and showed a net income (after paying fixed costs) of $6340. In August total sales were $375,000 with a net income of $10,250. 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) Version 2 Page 3

4 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 $526,000 and showed a net income (after paying fixed costs) of $16,074. In August total sales were $467,000 with a net income of $13,183. What are the real estate agency's fixed monthly costs? A) $22,883 B) $22,883 C) $25,774 D) $9700 E) $9700 Version 2 Page 4

5 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 $702,000 and showed a net income (after paying fixed costs) of $13,704. In August total sales were $226,000 with a net income of only $483. 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 $208,610 is the total monthly sales needed for the agency to break even. B) The horizontal intercept is about $243,390 is the total monthly sales needed for the agency to break even. C) The horizontal intercept is $208,610 and the net income for the agency when there are no sales. D) The horizontal intercept is $243,390 and the net income for the agency when there are no sales. E) The horizontal intercept is $684,610 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 $6400. 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 $48,700. 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 = 16,700 t B) Y = 6400 t+16,700 C) Y = 16,700 t 6400 D) Y = 16,700 t E) Y = 6400 t 16, Your family likes to eat fruit, but because of budget constraints, you spend only $4 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 Version 2 Page 5

6 14. Your family likes to eat fruit, but because of budget constraints, you spend only $9 each week on fruit. Your two choices are apples and grapes. Apples cost $0.50 per pound, and grapes cost $1.00 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) one pound B) two pounds C) three pounds D) one fourth pound E) half pound Version 2 Page 6

7 Answer Key 1. D 2. E 3. D 4. E 5. E 6. C 7. B 8. E 9. C 10. E 11. A 12. B 13. C 14. E Version 2 Page 7