Concept explainers
Reminder Round all answers to decimal places unless otherwise indicated.
Investing in the Stock Market You are considering buying three stocks whose prices at time t are given by
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FUNCTIONS AND CHANGE COMBO
- Mortgage Rates The following table is taken from the website of Freddie Mac. It shows rates for 30-year fixed-rate mortgages since 1970. y=Year r=Mortgagerate 1975 9.05 1980 13.74 1985 12.43 1990 10.13 1995 7.93 2000 8.05 2005 5.87 2010 4.69 2015 3.84 a. Explain in practical terms the meaning of r(2003). b. Use the table to estimate the value of r(2003).arrow_forwardPower Consumption: The figure shows the power consumption in San Francisco for a day in September (P is measured in megawatts; t is hours stating at midnight). (a) What was the power consumption at 6:00 A.M? At 6:00 P.m.? (b) When was the power consumption the lowest? (c) Find the net change in the power consumption from 9:00 A.M. to 7:00 P.M/arrow_forwardAn Uncertain Investment Suppose you invested 1300 in the stock market two years ago. During the first year the value of the stock increased by 12%. During the second year, the value of the stock decreased by 12%. How much money is your investment worth at the end of the two-year period? Did you earn money or lose money? Note: The answer to the first question is not 1300arrow_forward
- Computer Virus The number V of computers infected by a virus increases according to the model Vt=100e4.6052t, where t is the time in hours. Find the number of computers infected after (a) 1 hour, (b) 1.5 hours, and (c) 2 hours.arrow_forwardSales A company that produces snowboards forecasts monthly sales over the next 2 years to be S=23.1+0.442t+4.3cost6 where S is measured in thousands of units and t is the time in months, with t=1 corresponding to January 2017. Predict the sales for each of the following months. a February 2017 b February 2018 c June 2017 d June 2018arrow_forwardE-Filing The table shows the numbers of tax returns (in millions) made through e-file from 2007 through 2014. Let ft represent the number of tax returns made through e-file in the year t. (a) Find f2014f200720142007 and interpret the result in the context of the problem. (b) Make a scatter plot of the data. (c) Find a linear model for the data algebraically. Let N represent the number of tax returns made through e-file and let t=7 correspond to 2007. (d) Use the model found in part (c) to complete the table. (e) Compare your results from part (d) with the actual data. (f) Use a graphing utility to find a linear model for the data. Let x=7 correspond to 2007. How does the model you found in part (c) compare with the model given by the graphing utility?arrow_forward
- E-Filing The table shows the numbers of tax returns (in millions) made through e-file from 2007 through2014. Let f (t) represent the number of tax returns made through e-file in the year t. (a) Find f2014f200720142007 and interpret the result in the context of the problem. (b) Make a scatter plot of the data. (c) Find a linear model for the data algebraically. Let N represent the number of tax returns made through e-file and lett=7 correspond to 2007. (d) Use the model found in part (c) to complete the table. (e) Compare your results from part (d) with the actual data. (f) Use a graphing utility to find a linear model for the data. Let x=7 correspond to 2007. How does the model you found in part (c) compare with the model given by the graphing utility?arrow_forwardpH of Saliva The pH of saliva is normally in the range of 6.4 to 7.0. However, when a person is ill, the persons saliva becomes more acidic. a When Marco is sick, he tests the pH of his saliva and finds that it is 5.5. What is the hydrogen ion concentration of his saliva? b Will the hydrogen ion concentration in Marcos saliva increase or decrease as he gets better? c After Marco recovers, he tests the pH of his saliva, and it is 6.5. Was the saliva more acidic or less acidic when he was sick?arrow_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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