Concept explainers
Reminder Round all answer to two decimal places unless otherwise indicated.
Currency Conversion The number
a. What is the rate of change, or slope, of
b. A few days later, the American tourist went to a bank in Plymouth and exchange
c. Upon returning to the airport, she found that she found that she still had
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Chapter 3 Solutions
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
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Linear Algebra and Its Applications (5th Edition)
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- Reminder 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. 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. 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
- 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 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_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_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 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. Market Supply and demand The quality of wheat, in billions of bushels, that wheat suppliers are willing to produce in a year and offer for sale is called the quantity supplied and is denoted by S. The quantity supplied and is determined by the price P of wheat, in dollars per bushel, and the relation is P=2.13S0.75. The quantity of wheat, in billions of bushels, that wheat consumers are willing to purchase in a year is called the quantity demanded and is denoted by D. The quantity demanded is also determined by the price P of wheat, and the relation is P=2.650.55D. At the equilibrium price, the quality supplied and the quality demanded are the same. Find the equilibrium price for wheat.arrow_forward
- Reminder Round all answers to two decimal places unless otherwise indicated. 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 a 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 if the dairy has 30 cows. c. Calculate the value from part b.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_forwardReminder: Round all answer to two decimal places unless otherwise indicated. 15.Total Cost The total cost C for a manufacturer during a given time period is a function of the number N of items produced during that period. To deter mine a formula for the total cost, we need to know the manufacturers fixed costs covering things such as plant maintenance and insurance, as well as the cost for each unit produced, which is called the variable cost. To find the total cost, we multiply the variable cost by the number of items produced during that period and then add the fixed costs. Suppose that a manufacturer of widgets has fixed costs of 9000 per month and that the variable cost is 15 per widget so it costs 15 to produce 1 widget. a. Use a formula to express the total cost C of this manufacturer in a month as a function of the number of widgets produced in a month. Be sure to state the units you use. b. Express using functional notation the total cost if there are 250 widgets produced in a month, and then calculate that value.arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning