Reminder Round all the answers to two decimal places unless otherwise indicated.
Resistance in Copper Wire Electric resistance in copper wire changes with the temperature of the wire. If
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a. Use regression to find a
b. At what temperature is the electric resistance double that at
c. Suppose that you have designed a household appliance to be used at room temperature (
i. What resistance ratio do you predict at
ii. What range of resistance ratios represents plus or minus
iii. What temperature range for the appliance will ensure that your appliance operates within that
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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. The Dangers of Smoking Cigarette smoke contains any number of unhealthy substances, cyanide among them. One study modeled cyanide in the bloodstream after smoking a cigarette using C=0.1+0.3t0.6e0.17t, where C is the concentration of cyanide in the bloodstream, measured in nanograms per deciliter, and t is the time, in minutes, since smoking a cigarette. a. Make a graph of the concentration of cyanide during the first hour after smoking a cigarette. Add the line corresponding to the target level of 0.3 nanogram per deciliter. b. During which period is the concentration of cyanide 0.3 nanogram per deciliter or higher?arrow_forwardReminder Round all answers to decimal places unless otherwise indicated. Mileage for an Old Car The gas mileage M that you get on your car depends on its age t in years. a. Explain the meaning of dMdt in practical terms. b. As your car ages and its performance degrades, do you expect dMdt to be positive or negative?arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Length of Skid Marks Versus Speed When a car skids to a stop, the length L, in feet, of the skid marks is related to the speed S, in miles per hour, of the car by the power function L=130hS2. Here the constant h is the friction coefficient, which depends on the road surface. For dry concrete pavement, the value of h is about 0.85. a. If a driver going 55milesperhour on dry concrete jams on the brakes and skids to a stop. how long will the skid marks be? b. A policeman investigating an accident on dry concrete pavement finds skid marks 230feet long. The speed limit in the area is 60milesperhour. Is the driver in danger of getting a speeding ticket? c This part of the problem applies to any road surface, so the value of h is not known. Suppose you are driving at 60milesperhour, but, because of approaching darkness, you wish to slow to a speed that will cut your emergency stopping distance in half. What should your new speed be? Hint: You should use the homogeneity property of power functions here. By what factor should you change your speed to ensure that L changes by a factor of 0.5?arrow_forward
- ReminderRound 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. Sound Pressure and DecibelsSounds exerts a pressure P on the human ear. This pressure increases as the loudness of the sound increases. If the loudness D is measure in decibels and the pressure P is measured in dynes per square centimeter, then the relationship is give by P=0.00021.122D. a.Ordinary conversation has a loudness of about 65 decibels. What is the pressure exerted on the human ear by ordinary conversation? b.A decibel level of 120 causes pain to the ear and can result in damage. What is the corresponding pressure level on the ear?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_forwardReminder Round all answers to two decimal places unless otherwise indicated. Nail Growth The rate of fingernail growth depends on many factors, but in adults, nails grow at an average rate of 3 millimeters per month. If a nail is initially 12 millimeters long, find a formula that gives the length L, in millimeters, of the nail if left unclipped after t months.arrow_forward
- Reminder Round all answers to two decimal places unless otherwise indicated. Height of Tsunami WavesWhen waves generated by tsunamis approach shore, the height of the waves generally increases. Understanding the factors that contribute to this increase can aid in controlling potential damage to areas at risk. Greens law tells how water depth affects the height of a tsunami wave. If a tsunami wave has height H at an ocean depth D, and the wave travels to a location with water depth d, then the new height h of the wave is given by h=HR0.25, where R is the water depth ratio given by R=D/d. a. Calculate the height of a tsunami wave in water 25feet deep if its height is 3feet at its point of origin in water 15,000feet deep. b. If water depth decreases by half, the depth ratio R is doubled. How is the height of the tsunami wave affected?arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. The half life of 239U Uranium-239 is an unstable isotope of uranium that decays rapidly. In order to determine the rate of decay, 1 gram of 239U was placed in a container, and the amount remaining was measured at 1-minute intervals and recorded in the table below. Time, in minutes Grams remaining 0 1 1 0.971 2 0.943 3 0.916 4 0.889 5 0.863 a. Show that these are exponential data and find an exponential model For this problem, round all your answers to three decimal places. b. What is the percentage decay rate each minute? What does this number mean in practical terms? c. Use functional notation to express the amount remaining after 10 minutes and then calculate the value. d. What is the half life of 239U?arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Account Growth The table below shows the balance B in a savings account, in dollars, in terms of time t, measured as the number of years since the initial deposit was made. Time t Balance B 0 125.00 1 131.25 2 137.81 3 144.70 4 151.94 a. Was the yearly interest rate constant over the first 4 years? If so, explain why and find that rate. If not, explain why not. Round the ratios to two decimal places. b. Estimate B(2.75) and explain in practical terms what your answer means. Assume that interest is compounded and deposited continuously.arrow_forward
- Reminder: Round all answer to two decimal places unless otherwise indicated. 4.Thanksgiving Dinner It takes 10 minutes to preheat your oven to 325 degrees. For an oven preheated to 325 degrees, the recommended cooking time for a turkey is about 15 minutes per pound. a. Use a formula to express the total time T, in minutes, needed to preheat the oven and then bake a turkey weighing p pounds. b. Use your formula from part a to find the approximate time required to prepare a turkey weighing 18 pounds.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Decibels Sound exerts a pressure P on the human ear. This pressure increases as the loudness of the sound increases. It is convenient to measure the loudness D in decibels and the pressure P in dynes per square centimeter. It has been found that each increase of 1decibel in loudness causes a 12.2 increase in pressure. Furthermore, a sound of loudness 97decibels produces a pressure of 15 dynes per square centimeter. a. Explain why P is an exponential function of D and find the growth factor. b. Find P(0) and explain in practical terms what your answer means. c. Find an exponential model for P as a function of D. d. When pressure on the ear reaches a level of about 200 dynes per square centimeter, physical damage can occur. What decibel level should be considered dangerous?arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Kleibers law states that for the vast majority of animals, the metabolic rate M is a power function of the weight W, and the power is k=34. a.The Eastern gray squirrel weighs about 1 pound. How does the squirrels metabolic rate compare with that of a 200 -pound man? b.How does a 200- pound mans metabolic rate compare with that of a 130- pound woman? c.Based on your answer to part b, would overeating the same amount for each be more likely to lead to weight gain for the man or for the woman?arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning