The number of air safety inspectors for selected years is shown in the table. Year 1994 1995 1996 Inspectors 3345 3175 3099 (a) Find a linear function f that models these data. Is fexact or approximate? (b) Use f to estimate the number of inspectors in 2001. Compare your answer to the actual value of 3459. Did your estimate involve interpolation or extrapolation? ..... (a) A linear function f that models these data is f(x) =. (Round to the nearest integer as needed.) Is fexact or approximate? Choose the correct answer below. approximate exact (b) The estimate of the number of inspectors in 2001 is. (Simplify your answer. Type an integer or a decimal.) Compare the answer to the actual value of 3459. Choose the correct answer below. the estimated valu too high the estimated value is exact the estimated value is too low Did your estimate involve interpolation or extrapolation? Choose the correct answer below. interpolation extrapolation O O

The number of air safety inspectors for selected years is shown in the table. Year 1994 1995 1996 Inspectors 3345 3175 3099 (a) Find a linear function f that models these data. Is fexact or approximate? (b) Use f to estimate the number of inspectors in 2001. Compare your answer to the actual value of 3459. Did your estimate involve interpolation or extrapolation? ..... (a) A linear function f that models these data is f(x) =. (Round to the nearest integer as needed.) Is fexact or approximate? Choose the correct answer below. approximate exact (b) The estimate of the number of inspectors in 2001 is. (Simplify your answer. Type an integer or a decimal.) Compare the answer to the actual value of 3459. Choose the correct answer below. the estimated valu too high the estimated value is exact the estimated value is too low Did your estimate involve interpolation or extrapolation? Choose the correct answer below. interpolation extrapolation O O

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter3: Straight Lines And Linear Functions

Section3.3: Modeling Data With Linear Functions

Problem 7E: Tuition at American Public Universities This is a continuation of Exercise 6. The following table...

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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.
Tuition at American Public Universities This is a continuation of Exercise 6. The following table shows the average yearly in-state tuition and required fees, in dollars, charged by four-year American public universities in the school year ending in the given year. Date Average tuition 2012 8318 2013 8595 2014 8872 2015 9149 2016 9426 a. Show that these data can be modeled by a linear function, and find its formula. b. What is the slope for the linear function modeling tuition and required fees for public universities? c. What is the slope of the linear function modeling tuition and required fees for private universities? Note: See Exercise 6. d. Explain what the information in parts b and c tells you about the rate of increase in tuition in public versus private institutions. e. Which type of institution shows the larger percentage increase from 2015 to 2016? 6. Tuition at American Private Universities The following table shows the average yearly tuition and required fees, in dollars, charged by four-year American private nonprofit universities in the school year ending in the given year. Date Average tuition 2012 27, 870 2013 29, 004 2014 30, 138 2015 31, 272 2016 32, 406 a. Show that these data can be modeled by a linear function, and find its formula. b. Plot the data points and add the graph of the linear formula you found in part a. c. What prediction does this formula give for average tuition and fees at four-year American private nonprofit universities for the academic year ending in 2021?
Use your schools library, the Internet, or some other reference source to find real-life applications of approximations of functions.
bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.
Focal Length A refracting telescope has a main lens, or objective lens, and a second lens, the eyepiece see Figure 3.42. For a given magnification M of the telescope, the focal length F of the objective lens is a linear function of the focal length Fe of the eyepiece. For example, a telescope with magnification M=80 times can be constructed using various combinations of lenses. The following table gives some samples of focal length for telescopes with magnification M=80. Here focal lengths are in centimeters. Fe 0.3 0.5 0.7 0.9 F 24 40 56 72 a. Construct a linear model for the data. b. In this example, the magnification M is 80. In general, F is proportional to Fe, and the constant of proportionality is M. Use this relation to write a formula for F in terms of Fe and M. c. Solve the equation you obtained in part b for M and thus obtain a formula for magnification as a function of objective lens focal length and eyepiece focal length. d. To achieve a large magnification, how should the objective and eyepiece lenses be selected? FIGURE 3.42
Later 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.