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Evaluating a Step Function In Exercises 27-30, evaluate the function for the given values.
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Chapter 2 Solutions
EBK COLLEGE ALGEBRA
- High School Graduates The following table shows the number, in millions, graduating from high school in the United States in the given year. Year Number graduating in millions 1985 2.83 1987 2.65 1989 2.47 1991 2.29 a. By calculating difference, show that these data can be modeled using a linear function. b. What is the slope for the linear function modeling high school graduations? Explain in practical terms the meaning of the slope. c. Find a formula for a linear function that models these data. d. Express, using functional notation, the number graduating from high school in 1994, and then use your formula from part c to calculate that value.arrow_forwardEvaluate the function.arrow_forwardThe following table gives the cost, C(n)C(n), of producing a certain good as a linear function of nn, the number of units produced. Use the information in this table to answer the questions that follow it. nn (units) 75 100 125 150 C(n)C(n) (dollars) 10000 10125 10250 10375 (a) Evaluate each of the following expressions. Give economic interpretations of each. C(150)=C(150)= , which tells us C(150)−C(100)=C(150)−C(100)= , which tells us C(150)−C(100)150−100=C(150)−C(100)150−100= , which tells us (b)Estimate C(0)C(0). What is the economic significance of this value? (c)The fixed cost of production is the cost incurred before any goods are produced. The unit cost is the cost of producing an additional unit. Find a formula for C(n)C(n) in terms of nn, given that: Total cost=Fixed cost+Unit cost⋅Number of unitsTotal cost=Fixed cost+Unit cost⋅Number of units C(n)=arrow_forward
- Retirement For Pennsylvania state employees forwhom the average of the three best yearly salaries is$75,000, the retirement plan gives an annual pensionof 2.5% of 75,000, multiplied by the number of yearsof service. Write the linear function that models thepension P in terms of the number of years of service y.(Source: Pennsylvania State Retirement Fund)arrow_forwardA closed box with a square bottom has a total surface area (all 6 sides) of 400 square inches. Express the volume of the box as a function of w. 40² Recall that the volume of a box with dimensions width, length, height is the product of all three. h 0 W 11 Ov(w) = w(200 - w²) Ov(w) = w(100 - 2w²) ○ v(w) = w(200 – w²) Ov(w) = w(100 – w²) -w(400 – w²) O V(W) =arrow_forwardShow workarrow_forward
- Let A= {a,b,c,d,q,z} and B= {1,2,…,10} and define the function (D) how many functions are there from A to B? Briefly explain (E) how many one to one functions are there from A to B? Briefly explainarrow_forwardShow workarrow_forwardThe number of cells in a blue container doubles each day. The number of cells in a red container each day is shown in the table below. Day Number of Cells 1 50 75 100 125 150 175 7 200 A scientist creates functions to model the cell growth in both containers. Which statement about the functions is true? A.O The function for the blue container is linear, and the function for the red container is non-linear. B.O The functions for both containers are linear. C.O The function for the blue container is non-linear, and the function for the red container is linear. D.O The functions for both containers are non-linear. Copyright 20arrow_forward
- This table shows some input-output pairs for a function f. Use this information to determine the vertical intercept and the horizontal intercept of the function f. x f(x) 0 11 0.3 −2.9 1.2 −5 3 0 3.6 5 Vertical intercept = 0.3 and Horizontal intercept = −2.9 Vertical intercept = 3 and Horizontal intercept = 11 Vertical intercept = 3 and Horizontal intercept = 11 Vertical intercept = 0.3 and Horizontal intercept = 11 Vertical intercept = 11 and Horizontal intercept = 3arrow_forwardInput (x) 8 13 15 18 21 Output 11 14 21 (y) 2. A particular linear function has the table of values below. a. What is the rule that describes the function? b. Complete the table using the rule.arrow_forwardWrite the linear function that is represented in the following table. X 1 3 f(x) 11 7 3 -1arrow_forward
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