Evaluating a Step Function In Exercises 27-30, evaluate the function for the given values.
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Chapter 2 Solutions
Bundle: College Algebra, Loose-leaf Version, 10th + WebAssign Printed Access Card for Larson's College Algebra, 10th Edition, Single-Term
- 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_forwardFunction Barrow_forwardWhich table(s) can represent values of a function? Select all that apply.arrow_forward
- Evaluate 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_forwardRetirement 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_forward
- Show workarrow_forwardShow workarrow_forwardCollege Enrollment The total fall enrollment in 4-yearpublic institutions is given by y = 0.014x + 2.290,where x is the number of years after 1990 and y ismillions of students. Is this a linear function? Why orwhy not? What is the independent variable?(Source: U.S. Department of Education, National Center forEducation Statistics)arrow_forward
- In 2010, an investor put money into a fund. The graph below shows the value v = v(d) of the investment, in dollars, as a function of the date d. v(d) Investment value $305,000 $255,000- $205,000+ $155,000+ $105,000 $55,000- $5,000 2010 2020 2030 2040 2050 2060 d = Date Express the original investment using functional notation. 2010 ) Give the value of the above term. $ (b) Is the graph concave up or concave down? concave up concave down Explain what this means about the growth in value of the account. This means that the investment is increasing (c) In what year will the value of the investment reach $105,000? 2050 (d) What is the average yearly increase from 2050 to 2060? $ per year at an increasing ✓ Explain your reasoning. (e) Which is larger, the average yearly increase from 2050 to 2060 or the average yearly increase from 2010 to 2020? 2010 to 2020 2050 to 2060 The average yearly increase from 2010 to 2020 is $ rate. C. The average yearly increase from 2050 to 2060 is $arrow_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_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_forward
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