Concept explainers
Reminder Round all answer to two decimal places unless otherwise indicated.
Gasoline Prices In
a. Using
b. What price per gallon does the model yield for
c. Use the Internet to find the average price of gasoline for the current year. Does the model from part a give a price near the current price?
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Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
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- ReminderRound all answers to two decimal places unless otherwise indicated. TargetData from Targets 2014 annual report indicate that the equation of change for the revenue R, in millions of dollars, from 2010 through 2014 is dRdt=1647.7 where t is the time, in years, since 2010. If the initial revenue is 66,726.4 million dollars, find an equation that gives R as a linear function of t.arrow_forwardReminder Round all answer to two decimal places unless otherwise indicated. Poverty in the United States Form 2000 through 2014, the percentage of Americans living below the poverty level is given approximately by 5 P=11.36+0.28t, Where t is the time, in years, since 2000. a. According to this model, what percentage of Americans lived below the poverty level in 2010? The actual number is 15.1.) b. What is the slope of this linear function? c. Explain in practical terms the meaning of the slope you found in part b.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Getting Celsius Fro Fahrenheit Water freezes at 0 degrees Celsius, which is the same as 32 degrees Fahrenheit. Also, water boils at 100 degrees Celsius, which is the same as 212 degrees Fahrenheit. a. Use the freezing and boiling points of water to find a formula expressing Celsius temperature C as a linear function of the Fahrenheit temperature F b. What is the slope of the function you found in part a? Explain its meaning in practical terms. c. In Example 3.5, we showed that F=1.8C+32. Solve this equation for C and compare the answer with that obtained in part a.arrow_forward
- Reminder Round all answer to two decimal places unless otherwise indicated. Speed of Sounds The speed of sound in air changes with the temperature. When the temperature T is 32 degrees Fahrenheit, the speed S of sound is 1087.5 feet per second. For each degree increase in temperature, the speed of sound increases by 1.1 feet per second. a. Explain why speed S is a linear function of temperature T. Identify the slope of the function. b. Use a formula to express S as a linear function of T. c. Solve for T in the equation from part b to obtain a formula for temperature T as a linear function of speed S. d. Explain in practical terms the meaning of the slope of the function you found in part c.arrow_forwardReminder Round all answer to two decimal places unless otherwise indicated. Hair Growth When you are 18 years old you have a hair that is 14 centimeters long, and your hair grows about 12 centimeters each year. Let H(t) be the length, in centimeters, of that hair t years after age 18. a. Find a formula that gives H as a linear function of t. b. How long will it take for the hair to reach a length of 90 centimeters?arrow_forwardReminder Round all answer to two decimal places unless otherwise indicated. Currency Conversion The number P of British pounds that you can get from a bank is a linear function of the number D of American dollars you pay. An American tourist arriving at Heathrow airport in England went to a banking window at the airport and gave the teller 70 American dollars. She received 46 British pounds in exchange. In this exercise, assume that there is no service charge for exchanging currency. a. What is the rate of change, or slope, of P with respect to D? Explain in practical terms what this number means. Note: You need two values to calculate a slope, but you were given only one. If you think about it, you know one other value. How many British pounds can you get for zero American dollars? b. A few days later, the American tourist went to a bank in Plymouth and exchange 130 American dollars for British pounds. How many pounds did she receive? c. Upon returning to the airport, she found that she found that she still had 12.32 in British currency in her purse. In preparation for the trip home, she exchanged that for American dollars. How much money, in American dollars, did she get?arrow_forward
- Reminder Round all answer to two decimal places unless otherwise indicated. Budget Constraints Your family likes to eat fruit, but because of budget constraints, you spend only 5 each week on fruit. Your two choices are apples and grapes. Apples cost 1 per pound, and grapes cost 2 per pound. Let a denote the number f pounds of apples you buy and g the number of pounds of grapes. Because of your budget, it is possible to express g as a linear function of the variable a. To find the linear formula, we need to find its slope and initial value. a. If you buy one more pound of apples, how much less money do you have available to spend on grapes? Then how many fewer pounds of grapes can you buy? b. Use your answer to part a to find the slope of g as a linear function of a. Hint: Remember that the slope is the change in the function that results from increasing the variable by 1. Should the slope of g be positive or negative? c. To find the initial value of g, determine how many pounds of grapes you can buy if you buy no apples. d. Use your answer to parts b and c to find a formula for g as a linear function of a.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Cricket Chirps The temperature T in degrees Fahrenheit is approximately a linear function of the number C. of cricket chirps per minute. Twenty cricket chirps per minute corresponds to a temperature of 42 degrees Fahrenheit. Each additional chirp per minute corresponds to an increase of 0.25 degree. a. Use a formula to express T as linear function of C. b. What temperature is indicated by 100 cricket chirps per minute?arrow_forwardReminderRound all answers to two decimal places unless otherwise indicated. Minimum WageOn July 24, 2008, the federal minimum wage was 6.55perhour. On July 24, 2009, this wage was raised to 7.25perhour. If W(t) denotes the minimum wage, in dollars per hour, as function of time, in years, use the given information to estimate dWdt in 2009.arrow_forward
- Reminder Round all answer to two decimal places unless otherwise indicated. More on the Dairy This is a continuation of Exercise 1. The yearly income 1, in dollars, for the dairy comes from milk production, which depends on the number C of dairy cows. Each dairy cow produces 2500 gallons of milk per year, and the dairy sells milk for 2.00 per gallon. a. Find a formula that gives l as a linear function of C. b. Using the information from Exercise 1, determine the smallest number of cows the dairy needs in order to at least break even. Your answer should be a whole number. A Dairy A dairy spends 25,000 per year to maintain its barns and equipment. It costs 2000 per year to feed and care for each dairy cow. a. Using C for the number of dairy cows and E for the total yearly expense, in dollars, find formula that gives the total yearly expense as a linear function of the number of dairy cows. b. Use functional notation to express the total expense f the dairy has 30 cows. c. Calculate the value from part b.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Yellowfin Tuna Data were collected comparing the weight W, in pounds, of a yellowfin tuna to its length L, in centimeters. These data are presented in the following table. L=Length W=Weight 70 14.3 80 21.5 90 30.8 100 42.5 110 56.8 120 74.1 130 94.7 140 119 160 179 180 256 a. What is the average rate of change, in weight per centimeter of length, in going from a length of 100 centimeters to a length of 110 centimeters? b. What is the average rate of change, in weight per centimeter of length, in going from 160 to 180 centimeters? c. Judging from the data in the table, does an extra centimeter of length make more difference in weight for a small tuna or for a large tuna? d. Use the average rate of change to estimate the weight of a yellowtuna fish that is 167 centimeters long? e. What is the average rate of change, in length per pound of weight, in going from a weight of 179 pounds to a weight of 256 pounds? f. What would you expect to be the length of a yellow tuna weighing 225 pounds?arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. WendysAccording to a report in The Wall Street Journal, Wendys revenue fell 3.2 to 489.5million in the second quarter of 2015. That represents a quarterly decay rate, as a decimal of e0.0325. Let R(t) denote Wendys revenue, in millions of dollars, t quarters after the second quarter of 2015. Suppose that revenue continues to fall at this same rate. a.Write the equation of change for Wendys revenue. b.Find a formula that gives Wendys revenue t quarters after the second quarter of 2015.arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning