Concept explainers
Reminder Round all answers to two decimal places unless otherwise indicated.
Renting Motel Rooms You own a motel with
a. How much money do you charge per room if a group rents
b. Use a formula to give the rate you charge for each room if you rent
c. Find a formula for a function
d. Use functional notation to show the total revenue from renting a block of
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Chapter 1 Solutions
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Additional Math Textbook Solutions
Intermediate Algebra (13th Edition)
EBK ALGEBRA FOUNDATIONS
Beginning and Intermediate Algebra
Linear Algebra and Its Applications (5th Edition)
College Algebra (10th Edition)
Pre-Algebra, Student Edition
- Reminder Round all answer to two decimal places unless otherwise indicated. Real Estate Sales A real estate agency has fixed monthly costs associated with rent, staff salaries, utilities, and supplies. It earns its money by taking a percentage commission on total real estate sales. During the month of July, the agency had total sales of 832,000 and showed a net income after paying fixed costs of 15,704. In August, total sales were 326,000 with a net income of only 532. a. Use a formula to express net income as a linear function of total sales. Be sure to identify what the letters that you use mean. b. Plot the graph of net income and identify the slope and vertical intercept. c. What are the real estate agencys fixed monthly costs? d. What percentage commission does the agency take on the sale of a home? e. Find the horizontal intercept and explain what this number means to the real estate agency.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. The Fukushima Disaster On March 11, 2011, Japan suffered an earthquake and tsunami that caused a disastrous accident at the Fukushima nuclear power plant. Among many other results, amounts of iodine-131 that were 27 times the government limit were found in a sample of spinach 60 miles away?' Now, 27 times the government limit of iodine-131 is 54 thousand becquerels per kilogram." The following table shows the amount I, in thousands of becquerels per kilogram, of iodine-131 that would remain after t days. t=time,indays I=amountofiodine-131 0 54.00 1 49.52 2 45.41 3 41.64 4 38.18 a. Show that the data are exponential. In this part and the next, round to three decimal places b. Find an exponential model that shows the amount of iodine-131 present after t days. c. How long will it take for the amount of iodine-131 to fall to the government limit of 2 thousand becquerels per kilogram? Round your answer to the nearest whole day.arrow_forwardReminder Round all answer to two decimal places unless otherwise indicated. Digitized Pictures on a Disk Drive The hard disk drive on a computer holds 800 gigabytes of information. That is 800,000 megabytes. The formatting information, operating system, and applications software take up 6000 megabytes of disk space. The operator wants to store on his computer a collection of digitized pictures, each of which requires 2 megabytes of storage space. a. We think of the total amount of storage space used on the disk drive as a function of the number of pictures that are stored on the drive. Explain why this function in linear. b. Find a formula to express the total amount of storage space used on the disk drive as a linear function of the number of pictures that are stored on the drive. Be sure to identify what the letters you use mean. Explain in practical terms what the slope of this function is. c. Express using functional notation the total amount storage space used on the disk drive if there are 350 pictures stored on the drive, and then calculate that value. d. After putting a number of pictures on the disk drive, the operator executes a directory command, and at the end of the list, the computer displays the message 769, 000, 000, 000 bytes free. This message means that there are 769,000 megabytes of storage space left on the computer. How many pictures are stored on the disk drive? How many additional pictures can be added before the disk drive is filled?arrow_forward
- Reminder Round all answers to two decimal places unless otherwise indicated. More on investing You have 20, 000 for investment. You will invest S dollars in stocks and B dollars in bonds. You expect a 10 return on stocks and a 2 return on bonds. You want total return of 5 on your investment. a. The dollar amount of total return is 0.0520,000=1000. What is the dollar amount of return stocks and dollar amount for bonds? Suggestion: Yours answers will in volve the variables S and B. b. Write a system of two equations in two unknowns that determines how much will be invested in each category. Suggestion: One equation should show the total amount invested. The equation should show the total dollar return. c. Solve the system from part b to find the amount invested in stocks and the amount invested in bonds.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Insect ControlDDT dichlorodiphenyltrichloroethane was used extensively from 1940 to 1970 as an insecticide. It still sees limited use for control of disease. But DDT was found to be harmful to plants and animals, including humans, and its effects were found to be lasting. The amount of time that DDT remains in the environment depends on many factors, but the following table shows what can be expected of 100 kilograms of DDT that has seeped into the soil. t=time,inyearssinceapplication D=DDTremaining,inkilograms 0 100.00 1 95.00 2 90.25 3 85.74 a. Show that the data are exponential. b. Make a model of D as an exponential function of t. c. What is the half-life of DDT in the soil? That is, how long will it be before only 50 kilograms of DDT remain?arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Airspeed The airspeed of a plane is its speed in the absence of wind. With a headwind, ground speed the actual speed in relation to the ground is decreased by the speed of the wind. With a tailwind, ground speed is increased by the speed of the wind. Let A denote the airspeed of a plane and W the speed of the wind, both in miles per hour. Suppose it takes the plane 9 hours to travel the 720 miles from one town to another facing a headwind of W. the return trip, now with a tailwind of W, takes only 6 hours. a. Express the ground speed on the trip out in terms of A and W. b. Use the information from part a and the fact that distance equals rate times time to find an equation involving A and W for the trip out. c. Express the ground speed on the return trip in terms of A and W. d. Use the information from part c and the fact that distance equals rate times time to find an equation involving A and W for the return trip. e. Find the airspeed and the speed of the wind.arrow_forward
- Reminder Round all answers to two decimal places unless otherwise indicated. Catering a Dinner You are having a dinner catered. You pay a rental fee of 150 for the dining hall, and you pay the caterer 10 for each person who attends the dinner. a. Suppose you just want to break even. i.How much should you charge per ticket if you expect 50 people to attend? iiUse a formula to express the amount you should charge per ticket as a function of the number of people attending. Be sure to explain the meaning of the letters you choose and the units. iii.You expect 65 people to attend the dinner. Use your answer to part ii to express in functional notation the amount you should charge per ticket, and then calculate that amount. b. Suppose now that you want to make a profit of 100 from the dinner. Use a formula to express the amount you should charge per ticket as a function of the number of people attending. Again, be sure to explain the meaning of the letters you choose and the units.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Profit 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. In this exercise, we measure all monetary values in dollars. To determine a formula for the total cost, we need to know the manufacturers fixed costs covering such things 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. The total revenue R for a manufacturer during a given time period is also a function of the number N of items produced during that period. To determine a formula for the total monthly revenue, we need to know the selling price p per unit of the item, which in general is also a function of N. To find the total revenue, we multiply this selling price by the number of items produced. The profit P for a manufacturer is the total revenue minus the total cost. Suppose that a manufacturer of widgets has a fixed costs of 2000 per month and that the variable cost is 30 per widget. Further, the manufacturer has developed the following table showing the highest price p, in dollars, of a widget at which N widgets can be sold. Number N Price p 200 41.00 250 40.50 300 40.00 350 39.50 a.Use a formula to express the total monthly cost C of this manufacturer as a function of N. b.Use the table to find a linear model of p as a function of N. c.Use your answer to part b to find a formula expressing the total monthly revenue R as function of N. d.Use your answers to part a and part c to find a formula expressing the monthly profit P as a function of N. What type of function is the profit: linear or quadratic? e.Find the two monthly production levels at which the manufacturer just breaks even that is, where the profit is zero.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Paying Off a Credit Card You owe 8000 on a credit card. Because of the high balance, you stop charging and begin paying off the card. You can afford to make only the minimum monthly payment, which is 5 of the balance. The card carries an APR of 24. Under these conditions, the remaining balance alter t monthly payments is given by B=8000(1.020.95)tdollars, You feel comfortable resuming charging with the card when the balance is between 1000 and 2000. a. Plot the graph of B along with the target values of 1000 and 2000. Use a horizontal span of 0 to 100. b. For what values oft is the function B in the desired range? c. After how many monthly payments can you resume charging? Your answer should be a whole number.arrow_forward
- Reminder Round all answers to two decimal places unless otherwise indicated. A wedding Reception You rent a wedding venue for a cost of 3200. The cost includes a catered lunch for 50 guests. For each addition guest, though, the catered lunch costs 31. a. What is the cost of the venue and lunch if you invite 100 guests. b. Find a formula showing the cost of the venue and the lunch as a function of n, the number of guests. Assume that n is at least 50. c. The amount you have budgeted for the venue and catered lunch is 5500. How many guests can you invite.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. An Expensive Book A scientist visited Amazon.com to purchase a book. To his amazement, he found the book priced at 23,698,655.93. He discovered that there were two vendors selling this book on Amazon, and each was using a computer to adjust the price based on the other sellers price. The result was that each day the first vendors price was multiplied by 1.27. Assume that the initial price was 134.27, and determine how many days it took for the first vendors price to reach the exorbitant figure above. Round your answer to the nearest day.arrow_forwardReminder Round all answer to two decimal places unless otherwise indicated. Lean Body Weight in Males Your lean body weight L is the amount you would weigh if all the fat in your body were to disappear. One text gives the following estimate of lean body weight L in pounds for young adult males: L=98.42+1.08W4.14A, where W is total weight in pounds and A is abdominal circumference in inches. 7 a. Consider a group of young adult males who have the same abdominal circumference. If their weight increases but their abdominal circumference remains the same, how does their lean body weight change? b. Consider a group of young adult males who have the same weight. If their abdominal circumference decreases but their weight stays the same, how does their lean body weight change? c. Suppose a young adult male has a lean body weight of 144 pounds. Over a period of time, he gains 15 pounds in total weight, and his abdominal circumference increases by 2 inches. What is his lean body weight now?arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning