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Chapter 6 Solutions
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
- Reminder 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 answer to two decimal places unless otherwise indicated. Gasoline Prices In 1960, the average price per gallon of gasoline was 31 cents per gallon. Form 1960 to 2000, prices increased, on average, by 2.5 cents per gallon per year. 4 a. Using G for the price, in cents per gallon, and t for the time, in years, since 1960, use a formula to express G as linear function of t. b. What price per gallon does the model yield for 1990? Note: The actual price was 1.00 per gallon. 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?arrow_forwardReminder 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_forward
- Reminder 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 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_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. 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_forwardReminderRound all answers to two decimal places unless otherwise indicated. McDonaldsThe formula M(t)=1.19t+13.22 gives the approximate total revenue, in billions of dollars, for McDonalds t years after 2000. The formula applies to the years 2000 through 2013. a.What is the value of dMdt? Suggestion: Note that M is a linear function of t. b.Explain the meaning of the value you found in part a in practical terms.arrow_forwardReminder 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_forward
- Reminder Round all answers to two decimal places unless otherwise indicated. Male and Female High School Graduates The table below shows the percentage of male and female high school graduates who enrolled in college within 12 months of graduation. Years 1960 1965 1970 1975 Males 54 57.3 55.2 52.6 Females 37.9 45.3 48.5 49 a. Find the equation of the regression line for percentage of male high school graduates entering college as a function of time. b. Find the equation of the regression line for percentage of female high school graduates entering college as a function of time. c. Assume that the regression lines you found in part a and part b represent trends in the data. If the trends persisted, when would you expect first to have seen the same percentage of female and male graduates entering college? You may be interested to know that this actually occurred for the first time in 1980. The percentages fluctuated but remained very close during the 1981s and 1990s. In the 2000s, more female graduates entered college than did males. In 2008, for example, the rate for males was 66 compared with 72 for females.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_forwardReminder 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_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning