Concept explainers
Evaluating a Function In Exercises 9-20, evaluate the function at the given values of the independent variables. Simplify the results.
(a)
(b)
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(d)
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Student Solutions Manual For Larson/edwards? Multivariable Calculus, 11th
- 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_forwardLater High School Graduates This is a continuation of Exercise 16. 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 2001 2.85 2003 2.98 2005 3.11 2007 3.24 a. Find the slope of the linear function modeling high school graduations, and explain in practical terms the meaning of the slope. b. Find a formula for a linear function that models these data. c. Express, using functional notation, the number graduating from high school in 2008, and then calculate the value. d. The actual number graduating from high school in 1994 was about 2.52 million. Compare this with the value given by the formula in part b and with your answer to part of Exercise 16. Which is closer to the actual value? In general terms, what was the trend in high school graduations from 1985 to 2007? 16. High School Graduates The following table shows the number, in millions, graduating from high school in the United States in the given year.16 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_forwardMinimum Wage The table below is taken from the website of the U.S. Department of Labor. It shows the minimum wage for each decade from 1950 to 2010. The figures are adjusted for inflation and expressed in constant 2012 dollars. y=Year m=Minimumwage 1950 7.01 1960 7.59 1970 9.28 1980 8.46 1990 6.66 2000 6.90 2010 7.67 a. Find the value of m(1990). b. Use functional notation to express the minimum wage in 1985. c. Use the table to estimate the minimum wage in 1985. The actual value was 7.09.arrow_forward
- Modeling with Linear Functions Exercises 1 and 2: Write a symbolic representation (formula) for a func- tion f that calculates the following.arrow_forwardPrice of Silver The figure below shows the average price of silver for recent years. Let S(t) represent the average price (in dollars per ounce) of silver for year t. Source: kitco.com. Price of Silver S(t) 40 35 30 20 15+ 10+ 5+ ++++++ 2000 2002 2004 2006 2008 2010 2012 Year (a) Is S(t) a linear function? (b) What is the independent variable? (c) What is the dependent variable? (d) What is the domain of the function? (e) Estimate the range of the function. (f) What was the average price per ounce in 2008? (g) In what year was the average price $35 per ounce? Dollars per ouncearrow_forwardEasy calculus question, not graded. I will rate and like. Thank you for your work!arrow_forward
- Advanced Math K Complete parts (a)-(c). y = X y y= 1 -2 2 3 1 0 O Linear O Cubic 4 1 55 a) Find a cubic function that models the data in the table. Report the model with three decimal places. 6 14 0 b) Find a linear function that models the data. Report the model with three decimal places. c) Visually determine which model is the better fit for the data.arrow_forwardNumber 25 please. Intructions are in the second photo.arrow_forwardUsing the coffee demand function, Q = 8.56-p-0.4ps +0.1Y, show that sugar is a complement for coffee. You can use a numerical example, algebra, or calculus to do so. Let på be the price of sugar. Using calculus, (Enter your response rounded to one decimal place.) ƏQ apsarrow_forward
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