Concept explainers
Reminder Round all answer to two decimal places unless otherwise indicated.
Poverty in the United States Form
Where
a. According to this model, what percentage of Americans lived below the poverty level in 2010? (The actual number is
b. What is the slope of this linear function?
c. Explain in practical terms the meaning of the slope you found in part b.
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Chapter 3 Solutions
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Additional Math Textbook Solutions
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
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Beginning and Intermediate Algebra (6th Edition)
College Algebra with Modeling & Visualization (5th Edition)
Intermediate Algebra (7th Edition)
- 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. 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. 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_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_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. 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_forward
- 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_forwardReminder Round all answers to two decimals places unless otherwise indicated. Lines with the Same Slope On the same coordinate axes, draw two lines, each of slope 2. The first line has vertical intercept 1, and the second has vertical intercept 3. Do the lines cross? In general, what can you say about different lines with the same slope?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
- 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. High School GraduatesThe following table shows the number, in millions, graduating from high school in the United States in the given year. Year Number 1975 3.13 1980 3.04 1985 2.68 1990 2.57 1994 2.46 1999 2.76 2004 3.05 2009 3.32 a.Make a plot of the data and explain why a linear model is not appropriate. b.Use regression to find a linear model for the years 1975 through 1990. In this part and the next. round regression line parameters to three decimal places. c.Use regression to find a linear model for the years 1994 through 2009. d.Write a formula for a model of the number, in millions, graduating as a piecewise-defined function using the linear models from part b and part c. e.Make a graph of the formula you found in part d. f.The number graduating in 1995 was 2.52million. On the basis of your graph in part e, determine how this compares with what would be expected from your formula.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Magazine SalesThe following table shows the income from sales of a certain magazine, measured in thousands of dollars, at the start of the given year. Year Income 2009 7.76 2010 8.82 2011 9.88 2012 10.94 2013 12.00 2014 13.08 2015 14.26 2016 15.54 Over an initial period the sales grew at a constant rate, and over the rest of the time the sales grew at a constant percentage rate. Calculate differences and ratios to determine what these time periods are, and find the growth rate or percentage growth rate, as appropriate.arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning