Concept explainers
Reminder 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
Want to see the full answer?
Check out a sample textbook solutionChapter 4 Solutions
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
- 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. 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. World Copper Production World production of copper, in millions of tons per year, from 1900 to 2000 is given by C=0.51.033t, where t is the time in years since 1900. a.What production level does this model give for the year 2000? b.If this model were extended to 2025, how could you use your knowledge of copper production in 2024 to estimate copper production in 2025?arrow_forward
- Reminder Round all answers to two decimal places unless otherwise indicated. Quarterly Pine Pulpwood PricesIn southwest Georgia, the average pine pulpwood prices vary predictably over the course of the year, primarily because of weather. Prices in 2009 followed this pattern. At the beginning of the first quarter, the average price P was 9 per ton. During the first quarter, prices declined steadily to 8 per ton, then remained steady at 8 per ton through the end of the third quarter. During the fourth quarter, prices increased steadily from 8 to 10 per ton. a.Sketch a graph of pulpwood prices as a function of the quarter in the year. b.What formula for price P as a function of t, the quarter, describes the price from the beginning of the year through the first quarter? c.What formula for price P as a function of t, the quarter, describes the price from the first to the third quarter? d.What formula for price P as a function of t, the quarter, describes the price from the third to the fourth quarter? e.Write a formula for price P throughout the year as a piecewise-defined function of t, the quarter.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_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_forward
- Reminder Round all answers to two decimal places unless otherwise indicated. Renting Motel Rooms You own a motel with 30 rooms and have a pricing structure that encourages rentals of rooms in groups. One room rents for 85.00, two for 83.00 each, and in general the group rate per room is found by taking 2 off the base of 85 for each extra room rented. a.How much money do you charge per room if a group rents 3 rooms? What is the total amount of money you take in? b.Use a formula to give the rate you charge for each room if you rent n rooms to an organization. c.Find a formula for a function R=R(n) that gives the total revenue from renting n rooms to a convention host. d.Use functional notation to show the total revenue from renting a block of 9 rooms to a group. Calculate that value.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Recent EarthquakesOn April 25, 2015, an earthquake of magnitude 7.8 on the Richter scale struck Nepal. On May 12, 2015, a major aftershock of magnitude 7.3 on the Richter scale shook the same region. a. How did the power of the first earthquake and this aftershock compare? b. What would be the magnitude of a quake twice as powerful as the first quake?arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. WendysAccording to a report in The Wall Street Journal, Wendys revenue fell 3.2 to 489.5million in the second quarter of 2015. That represents a quarterly decay rate, as a decimal of e0.0325. Let R(t) denote Wendys revenue, in millions of dollars, t quarters after the second quarter of 2015. Suppose that revenue continues to fall at this same rate. a.Write the equation of change for Wendys revenue. b.Find a formula that gives Wendys revenue t quarters after the second quarter of 2015.arrow_forward
- Reminder 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_forwardReminder Round all answers to two decimal places unless otherwise indicated. Inflation The yearly inflation rate tells the percentage by which prices increase. For example, from 1990 through 2000, the inflation rate in the United States remained stable at amount 3 per year. In 1990, an individual retired on a fixed income of 36,000 per year. Assuming that the inflation rate remains at 3, determine how long it will take for the retirement income to deflate to half its 1990 value. Note: To say that retirement income has deflated to half its 1990 value means that prices have doubled.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Cleaning Contaminated Water A tank of water is contaminated with 60 pounds of salt. In order to bring the salt concentration down to a level consistent with EPA standards, clean water is being piped into tank, and the well-mixed overflow is being collected for removal to a toxic-waste site. The result is that at the end of each hour, there is 22 less salt in the tank than at the beginning of the hour. Let S=S(t) denote the number of pounds of salt in the tank t hours after the flushing process begins. a. Explain why S is an exponential function and find its hourly decay factor. b. Give a formula for S. c. Make a graph of S that shows the flushing process during the first 15 hours, and describe in words how the salt removal process progresses. d. In order to meet EPA standards, there can be no more than 3 pounds of salt in the tank. How long must the process continue before EPA standards are met? e. Suppose this cleanup procedure costs 8000 per hour to operate. How much does it cost to reduce the amount of salt from 60 pounds to 3 pounds? How much does it cost to reduce the amount of salt from 3 pounds to 0.1 pound?arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning