Concept explainers
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
a. Explain why speed
b. Use a formula to express
c. Solve for
d. Explain in practical terms the meaning of the slope of the function you found in part
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Chapter 3 Solutions
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
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High School Math 2015 Common Core Algebra 1 Student Edition Grade 8/9
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- Reminder 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_forwardReminderRound 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. 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. 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. 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_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_forward
- ReminderRound 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_forwardReminderRound all answers to two decimal places unless otherwise indicated. DensityThe total weight of a rock depends on its size and is proportional to its density. In this context, density is the weight per cubic inch. Let w denote the weight of the rock in pounds, s the size of the rock in cubic inches, and d the density of the rock in pounds per cubic inch. a. What is the total weight of a 3-cubic-inch rock that weighs 2 pounds per cubic inch? b. Write an equation that shows the proportionality relation. What is the constant of proportionality? c. Use the equation you found in part b to find the total weight of a 14-cubic-inch rock with density 0.3 pound per cubic inch.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
- ReminderRound all answers to two decimal places unless otherwise indicated. Skirt LengthOne authors analyzed skirt lengths in the United Kingdom UK and Germany. To get a standardized measure of skirt length, she calculated the ratio. LengthfromshouldertoskirthemLengthfromshouldertoankle The article includes the following graph of the ratio for skirt length in terms of the year. In the graph, the solid line is the ratio in the UK, and the dashed line is the ratio in Germany. FIGURE 1.32 Ratio for skirt length a.Does a larger ratio indicate a longer or a shorter skirt? b.When were skirt lengths shortest in the UK? c.In this period, did skirt lengths in either Germany or the UK ever reach to the ankle?arrow_forwardReminderRound all answers to two decimal places unless otherwise indicated. InflationDuring a period of high inflation, a political leader was up for re-election. Inflation had been increasing during his administration, but he announced that the rate of increase of inflation was decreasing. Draw a graph of inflation versus time that illustrates this situation. Would this announcement convince you that economic conditions were improving?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