Concept explainers
Reminder Round all answers to two decimal places unless otherwise indicated.
8. Cell Phone Charges One cell phone plan charges a flat monthly rate of
a. Choose letters to represent the variables.
b. Write a formula to express the cell phone charges as a function of the number of text messages (assume that the number is at least
c. Use functional notation to show the cost of the cell phone if you have
d. Write the formula to express the cell phone charges, this assuming that the number of text messages is less than
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Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
- Reminder: 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_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_forwardReminder Round all answers to two decimal places unless otherwise indicated. High School Graduates The following table shows the number, in millions, graduating from high school in the United States, in the given year. t=Year N= Number graduating 1985 2.83 1987 2.65 1989 2.47 1991 2.29 a. Explain in practical terms what N(1989) means, and find its value. b. Use functional notation to express the number of graduates in 1988, and estimate its value. c. Find the average rate of change per year during the period 1989 to 1991. d. Estimate the value of N(1994).arrow_forward
- ReminderRound all answers to two decimal places unless otherwise indicated. An InvestmentIn 2010, an investor put money into a fund. The graph in Figure 1.26 shows the value, v=v(d) of the investment, in dollars, as a function of date d. a.Express the original investment using functional notation and give its value. b.Is the graph concave up or concave down? Explain what this means about the growth in value of the account. c.When will the value of the investment reach 55,000? FIGURE 1.26 An investment d.What is the average yearly increase from 2050 to 2060? e.Which is larger, the average yearly increase from 2050 to 2060 or the average yearly increase from 2010 to 2020? Explain your reasoning.arrow_forwardReminder: Round all answer to two decimal places unless otherwise indicated. a. Calculate the rental charge if you rent a car for 2 days and drive 100 miles. b. Use a formula to express the cost of renting a car as a function of the number of days you keep it and the number of miles you drive. Identify the function and each variable you use, and state the units. c. It is about 250 miles from Dallas to Austin. Use functional notation to express the cost to rent a car in Dallas, drive it to Austin, and return it in Dallas 1 week later. Use the formula from part b to calculate the cost.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
- ReminderRound 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. 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 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_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 decimal places unless otherwise indicated. 9. Cell Phone Charges Again One cell phone plan charges a flat monthly rate of 34.95 with extra charges of 0.35 per minute for each minute after the first 4000 minutes and 0.10 per text message after the first 100 text messages. a. Choose letters to represent the variables. b. Write a formula to express the cell phone charges as a function of the number of minutes used assume that the number is at least 4000 and the number of text messages assume that the number is at least 100. c. What are your cell phone charges if you use 6000 minutes and 450 text messages? d. Write the formula to express the cell phone charges, this assuming that the minutes are at least 4000, but the number of text message is less than 100. e. What are your cell phone charges if you use 4200 minutes and 88 text messages?arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Note Some of the formulas below use the special number e, which was presented in the Prologue. The height of the winning pole vault in the early years of the modern Olympic Games can be modeled as a function of time by the formula H=0.05t+3.3 Here t is the number of years since 1900, and H is the winning height in meters. One meter is 39.37 inches. a. Calculate H(4) and explain in practical terms what your answer means. b. By how much did the height of the winning pole vault increase from 1900 to 1904? From 1904 to 1908?arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning