Concept explainers
Reminder Round all answers to two decimal places unless otherwise indicated.
Tornadoes In Oklahoma The graph in Figure
Round your answers to the nearest whole number.
a. When were the most tornadoes reported? How many were reported in that year?
b. When were the fewest tornadoes reported? How many were reported in that year?
c. What was the average yearly rate of decrease in tornadic activity from
d. What was the average yearly rate of increase in tornadic activity from
e. What was the average yearly rate of change (that is, the average yearly rate of total increase or total decrease) in tornadic activity from
FIGURE
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Chapter 1 Solutions
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
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- Reminder 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_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 answers to two decimal places unless otherwise indicated. The Rock with a Formula If from ground level we toss a rock upward with a velocity of 30feetpersecond, we can use elementary physics to show that the height in feet of the rock above the ground t seconds after the toss is given by S=30t16t2. a. Use your calculator to plot the graph of S versus t. b. How high does the rock go? c. When does it strike the ground? d. Sketch the graph of the velocity of the rock versus time.arrow_forward
- Reminder 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. HydrographsWhen a rainfall brings more water than the soil can absorb, runoff occurs, and hydrologists refer to the event as a rainfall excess. The easiest way to envision runoff is to think of a watershed that drains into the mouth of a single stream. The runoff is the number of cubic feet per minute cfpm being dumped into the mouth of the stream. An important way of depicting runoff is the hydrograph, which is simply the graph of total discharge, in cubic feet per minute, versus time. A typical runoff hydrograph is shown in Figure 1.47. The horizontal axis is hours since rainfall excess began. A hydrograph displays a number of important features. a. Time to peak is the elapsed time from the start of rainfall excess to peak runoff. What is the time to peak shown by the hydrograph in Figure 1.47? b. Time of concentration is the elapsed time from the end of rainfall excess to the inflection point after peak runoff. The end of rainfall excess is not readily apparent from a hydrograph, but it occurs before the peak. If the end of rainfall excess occurred 5 hours after the start of rainfall excess. estimate the time of concentration from Figure 1.47. c. Recession time is the time from peak runoff to the end of runoff. Estimate the recession time for the hydrograph in Figure 1.47. d. Time base is the time from beginning to end of surface runoff. What is the time base for the hydrograph in Figure 1.47? FIGURE 1.47 A runoff hydrographarrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Moores Law The speed of a computer chip is closely related to the number of transistors on the chip, and the number of transistors on a chip has increased with time in a remarkably consistent way. In fact, in the year 1965, Dr. Gordon E. Moore now chairman emeritus of Intel Corporation observed a trend and predicted that it would continue for a time. His observation, now known as Moores law, is that every two years or so a chip is introduced with double the number of transistors of its fastest predecessor. This law can be restated in the following way: If time increases by 1year, then the number of transistors is multiplied by 100.15.More generally, the rule is that if time increases by tyears, then the number of transistors is multiplied by 100.15t.For example, after 8years, the number of transistors is multiplied by 100.158, or about 16. The 6th generation Core processor was released by Intel Corporation in the year 2015. a.If a chip were introduced in the year 2022, how many times the transistors of the 6th generation Core would you expect it to have? Round your answer to the nearest whole number. b.The limit of conventional computing will be reached when the size of a transistors on a chip will be 200 times that of the 6th generation Core. When, according to Moores law, will that limit be reached? c.Even for unconventional computing, the law of physics impose a limit on the speed of computation. The fastest speed possible corresponds to having about 1040 times the number of transistors as on the 6th generation Core. Assume that Moores law will continue to be valid even for unconventional computing, and determine when this limit will be reached. Round your answer to the nearest century.arrow_forward
- ReminderRound all answers to two decimal places unless otherwise indicated. Wind ChillThe graph in Figure 1.40 shows the temperature T = Tv adjusted for wind chill as a function of the velocity v of the wind when the thermometer reads 30 degrees Fahrenheit. The adjusted temperature T shows the temperature that has an equivalent cooling power when there is no wind. a. At what wind speed is the temperature adjusted for wind chill equal to 0? b. Your answer in part a is the solution of an equation involving Tv. Which equation? c. At what value of v would a small increase in v have the greatest effect on Tv? In other words, at what wind speed could you expect a small increase in wind speed to cause the greatest change in wind chill? Explain your reasoning. d. Suppose the wind speed is 45 miles per hour. Judging from the shape of the graph, how significant would you expect the effect on Tv to be if the wind speed increased? FIGURE 1.40 Temperature adjusted for wind chill when the thermometer reads 30 degrees Fahrenheit.arrow_forwardReminder 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_forward
- Reminder 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_forwardReminder Round all answers to two decimal places unless otherwise indicated. Estimating Wave Height Sailors use the following function to estimate wave height h, in feet, from wind speed w, in miles per hour h=0.02w2 a. Make a graph of wave height versus wind speed. Include wind speeds of up to 25 miles per hour. b. A small boat can sail safely provided wave heights are no more than 4 feet. What range of wind speed will give safe sailing for this boat?arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Marriage Length In this exercise, we consider data from the Statistical Abstract of the United States on the fraction of women married for the first time in 1960 whose marriage reached a given anniversary number. The data show that the fraction of women who reached their fifth anniversary was 0.928. After that, for each one-year anniversary number, the fraction reaching that number drops by about 2. These data describe constant percentage change, so it is reasonable to model the fraction M as an exponential function of the number n of anniversaries since fifth. a.What is the yearly decay factor for the exponential model? b.Find an exponential model for M as a function of n. c.According to your model, what fraction of women married for the first time in 1960 celebrated their 40th anniversary? Take n=35. Round your answer to three decimal places. The actual fraction is 0.449 or 44.9.arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning