Concept explainers
Demand for Mobile Data The following table shows the worldwide demand for mobile smartphone data in terms of its price per megabyte (MB):38
Price p ($/MB) | 0.01 | 0.03 | 0.06 | 0.10 | 0.20 | 0.46 |
Demand q (MB/smartphone user) | 4,000 | 1,000 | 700 | 500 | 300 | 150 |
Which of the following kinds of models would best fit the given data? Explain your choice of model. (A, a, b, and c are constants.)
(A)
(B)
(C)
(D)
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Finite Mathematics
- Energy ConsumptionThe monthly residential consumption of energy in the U.S. for 2012 is found in the following table. Source: Energy Information Administration. Month Energytrillion BTU January 990.527 February 833.163 March 560.826 April 412.426 May 297.500 June 253.015 July 240.486 August 248.035 September 249.354 October 378.094 Number 631.203 December 838.265 Plot the data, letting t=1 correspond to January, t=2 to February, and so on. Is it reasonable to assume that the monthly consumption of energy is periodic? Find the trigonometric function of the form C(t)=asin(bt+c)+d that models these data when t is the month of the year and C(t) is the energy consumption. Graph the function on the same calculator window as the data. Estimate the total energy consumption for the year for residential customers in the United States and compare it to the actual value. Calculate the period of the function found in part b. Is this period reasonable?arrow_forwardDemand for Candy Bars In this problem you will determine a linear demand equation that describes the demand for candy bars in your class. Survey your classmates to determine what price they would be willing to pay for a candy bar. Your survey form might look like the sample to the left. a Make a table of the number of respondents who answered yes at each price level. b Make a scatter plot of your data. c Find and graph the regression line y=mp+b, which gives the number of respondents y who would buy a candy bar if the price were p cents. This is the demand equation. Why is the slope m negative? d What is the p-intercept of the demand equation? What does this intercept tell you about pricing candy bars? Would you buy a candy bar from the vending machine in the hallway if the price is as indicated. Price Yes or No 50 75 1.00 1.25 1.50 1.75 2.00arrow_forwardGrade Point Average In many universities students are given grade points for each credit unit according to the following scale: A 4 points B 3 points C 2 points D 1 point F 0 point For example, a grade of A in a 3-unit course earns 43=12 grade points and a grade of B in a 5-unit course earns 35=15 grade points. A students grade point average GPA for these two courses is the total number of grade points earned divided by the number of units; in this case the GPA is (12+15)8=3.375. a Find a formula for the GPA of a student who earns a grade of A in a units of course work, B in b units, C in c units, D in d units and F in f units. b Find the GPA of a student who has earned a grade of A in two 3-unit courses, B in one 4-unit courses and C in three 3-unit courses.arrow_forward
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