Concept explainers
Reminder Round all answers to two decimal places unless otherwise indicated.
A Bald Eagle Murder Mystery At 3:00 P.M., a park ranger discovered a dead bald eagle that had been impaled by an arrow. Only two archers were round in the region. The first archer is able to establish that between 11:00 A.M. and 1:00 P.M. he was in a nearby diner having lunch. The second archer can show that he was in camp with friends between 9:00 A.M. and 11:00 A.M. The air temperature in the park has remained at a constant 62 degrees. Beginning at 3:00 P.M. the difference
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This table, together with the fact that the body temperature of a living bald eagle is 105 degrees, exonerates one of the archers but the other may remain a suspect. Which archer’s innocence is established?
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Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
- Reminder Round all answers to two decimal places unless otherwise indicated. Sleeping Longer A certain man observed that each night he was sleeping 15 minutes longer than he had the night before, and he used this observation to predict the day of his death. 9 If he made his observation right after sleeping 8 hours, how long would it be until he slept 24 and so would never again wake?arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Walking and Running You live east of campus, and you are walking from campus toward your home at a constant speed. When you get there, you rest for 5minutes and then run back west at a rapid speed. After a few minutes, you reach your destination, and then you rest for 10minutes. Measure your location as your distance west of your home, and make graphs of your location and velocity.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
- Reminder Round all answers to two decimal places unless otherwise indicated. Drug Concentration When a drug is administered orally, it takes some time before the blood concentration reaches its maximum level. After that time, concentration levels decrease. When 500 milligrams of procainamide is administered orally, one model for a particular patient gives blood concentration C, in milligrams per liter, after t hours as C=2.65(e0.2te2t) During what time period is the drug concentration level at least 1.5 milligrams per liter?arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Newtons Law of Cooling says that a hot object cools rapidly when the difference between its temperature and that of the surrounding air is large, but the object cools more slowly when it nears room temperature. Suppose a piece of aluminum is removed from an oven and left to cool. The following table gives the temperature A=A(t), in degrees Fahrenheit. of the aluminum t minutes after it is removed from the own. a.Explain the meaning of A(75) and estimate its value. b.Find the average decrease of temperature pet minute during the first half-hour of cooling. t=Minutes A=Temperature 0 302 30 152 60 100 90 81 120 75 150 73 180 72 210 72 c.Find the average decrease per minute of temperature during the first half of the second hour of cooling. d.Explain how parts b and c support Newtons law of cooling. e.Use functional notation to express the temperature of the aluminum after I hour and 13 minutes. Estimate the temperature at that time. Note: Your work in part c should be helpful. f.What is the temperature of the oven? Exams your answer using functional notation, and give its value. g.Explain why you would expect the function A to have a limiting value. h.What is roan temperature? Explain your reasoning.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. There is a formula that estimates how much your puppy will weigh when it reaches adulthood. The method we present applies to medium-sized breeds. First, find your puppys weight w, in pounds, at an age of a weeks, where a is 16 weeks or less. Then the predicted adult weight W=W(a,w) in pounds, is given by the formula. W=52wa a. Use functional notation to express the adult weight of a puppy that weighs 6 pounds at 14 weeks. b. Calculate the predicted adult weight for the puppy from part a.arrow_forward
- Reminder Round all answers to two decimal places unless otherwise indicated. TravelIng in a CarMake graphs of location and velocity for each of the following driving events. In each case, assume that the car leaves from home moving west down a straight road and that position is given as the distance west from home. a. A vacation: Being eager to begin your overdue vacation, you set your cruise control and drive faster than you should to the airport. You park your car there and get on an airplane to Spain. When you fly back 2 weeks later, you are tired, and you drive back home at a leisurely pace. Note: Here we are talking about the location of your car, not of the airplane. b. On a country road: A car driving down a country road encounters a deer. The driver slams on the brakes, and the deer runs away. The journey is cautiously resumed. c. At the movies: In a movie chase scene, our hero is driving his car rapidly toward the bad guys. When the danger is spotted, he does a Hollywood 180-degree turn and speeds off in the opposite direction.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. A Roast is taken from the refrigerator where it had been for several days and placed immediately in a preheated oven to cook. The temperature R=R(t) of the roast t minutes after being placed in the oven is given by R=325280e0.005tdegreesFahrenheit a. What is the temperature of the refrigerator? b. Express the temperature of the roast 30 minutes after being put in the oven in functional notation, and then calculate its value. c. By how much did the temperature of the roast increase during the first 10 minutes of cooking? d. By how much did the temperature of the roast increase from the first hour to 10 minutes after the first hour of cooking?arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. A Rubber Ball A rubber ball is dropped from the top of a building. The ball lands on concrete and bounces once before coming to rest on the grass. Measure the location of the ball as its distance up from the ground. Make graphs of the location and velocity of the ball.arrow_forward
- ReminderRound 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_forwardReminderRound all answers to two decimal places unless otherwise indicated. NoteSome of the formulas below use the special number e, which was presented in the Prologue. Mitscherlichs EquationAn important agriculture problem is to determine how a quantity of nutrient, such as nitrogen, affects the growth of plants. We consider the situation wherein sufficient quantities of all but one nutrient are present. One boule of a nutrient is the amount needed to produce 50 of maximum possible yield. In 1990, E.A. Mitscherlichs proposed the following relation, which is known as Mitscherlichs Equation: Y=10.5b. Here b is the number of baules of nutrient applied, and Y is the percentage as a decimal of maximum yield produced. a.Verify that the formula predicts that 50 of maximum yield will be produced if 1 baule of nutrient is applied. b.Use functional notation to express the percentage of maximum yield produced by 3 baule of nutrient, and calculate the value. c.The exact value of a baule depends on the nutrient in question. For nitrogen, 1 baule is 223 pounds per acre. What percentage of maximum yield will be produced if 500 pounds of nitrogen per acre is present?arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning