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_forwardWhich table(s) can represent values of a function? Select all that apply.arrow_forwardEvaluate the function.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_forwardThe daily cost to a printer is modeled by the function C(x) = 4x + 1400 where C(x) is the total daily cost and is the number of copies printed. Find C(7000), and interpret its meaning. C(7000) | Enter an integer or decimal number [more..] This value represents O The product of the daily cost and the number of copies O The number of copies manufactured when the daily cost is 7000 O The daily cost when 7000 copies are printed Check Answer masa Σarrow_forwardShow workarrow_forward
- College 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_forwardIn 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_forwardThis 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_forward
- 9 grade math. Function notation. Evaluate each function.arrow_forward* The total number of cars in a dealership is modeled by f(x) = 4x² - 2x, where x represents the number of rows of cars. How many rows are there in the dealership if it has a total of 650 cars? AX A 12 Ax B 13 C 10 D 8 Progress Learning 2024, All Rights Reserved. Terms | Privacy PHONE 1-877-377-9537 | FAX 1-877-816-0808 Blog MacBook Proarrow_forwardThe price of a stock starts at $60 per share. The stock price rises at an average rate of $0.75 per day for the first 30 days the stock is available. Jason bought 200 shares of the stock at its initial price of $60 per share. He sold 100 shares of the stock after x days, where x is a positive integer less than 29. He sold the remaining 100 shares the following day. Which of the following functions f models Jason's total profits in dollars after selling all 200 shares of his stock? () A. f(x) = 100x – 75 B. f(x) = 100x + 75 C. f(x) = 150x – 75 D. f(x) = 150x + 75arrow_forward
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