Concept explainers
Reminder Round all answers to two decimal places unless otherwise indicated.
Note Some of the formulas below use the special number
10.Flushing Chlorine City water, which is slightly chlorinated, is being used to flush a tank of heavily chlorinated water. The concentration
a. What is the initial concentration of chlorine in the tank?
b. Express the concentration of chlorine in the tank after 3 hours using functional notation, and then calculate its value.
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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 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. 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_forward
- Reminder Round all answers to two decimal places unless otherwise indicated. Ship Propellers An ideal diameter d, in feet, of a ships propeller is given by the formula d=ch1/5r3/5. Here h is the horsepower of the engine driving the propeller. r is the maximum number of revolutions per minute of the propeller, and c is a constant. In both parts, give your answer in terms of a percentage. a. If the horsepower is increased by 20 while the number of revolutions per minute remains the same, how is the propeller diameter affected? b. If the horsepower remains the same while the number of revolutions per minute is increased by 20, how is the propeller diameter affected?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. 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_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. Yield Response to Several Growth FactorsThis is a continuation of Exercise 23. If more than one nutrient is considered, the formula for percentage of maximum yield is a bit more complex. For three nutrients, the formula is Y(b,c,d)=(10.5b)(10.5c)(10.5d). a.Express using functional notation the percentage of maximum yield produced from 1 baule of the first nutrient, 2 baules of the third nutrient, and 3 baules of the third nutrient, and then calculate that value. b.One baule of nitrogen is 223 pounds per acre, 1 baule of phosphorus is 45 per acre, and 1 baule of potassium is 76 pounds per acre. What percentage of maximum yield will be obtained from 200 pounds of nitrogen per acre, 100 pounds of phosphorus per acre, and 150 pounds of potassium per acre? 23. 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_forwardReminder Round all answers to two decimal places unless otherwise indicated. Waiting at a Stop SignConsider a side road connecting to a major highway at a stop sign. According to a study by D.R. Drew, the average delay D, in seconds, for a car waiting at the stop sign to enter the highway is given by D=eqt1qtq, where q is the flow rate, or the number of cars per second passing the stop sign on the highway, and T is the critical highway that will allow for safe entry. We assume that the critical headway is T=5seconds. a.What is the average delay time if the flow rate is 500 cars per hour 0.14 car per second? b.The service rate s for a stop sign is the number of cars per second that can leave the stop sign. It is related to the delay by s=D1. Use function composition to represent the service rate as a function of flow rate. Reminder:(a/b)1=b/a. c.What flow rate will permit a stop sign service rate of 5 cars per minute 0.083 car per second?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
- 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 decimal places unless otherwise indicated. Hiking You are hiking in a hilly region, and E=E(t) is your elevation at time t. a. Explain the meaning of dEdt in practical terms. b. Where might you be when dEdt is a large positive number? c. You reach a point where dEdt is briefly zero . Where might you be? d. Where might you be when dEdt is a large negative number?arrow_forwardReminder: Round all answer to two decimal places unless otherwise indicated. 3.Fat in Fast Food You are shopping for dinner for your family in a fast-food restaurant, but you are concerned about fat. An informative menu gives you the following information. Item Hamburger Chicken Sandwich Fries Onion rings Grams of fat 24 13 30 25 a. How much total fat is in an order of 3 hamburgers, 1 chicken sandwich, 2 orders of fries, and 2 orders of onion rings? b. Use a formula to express the total grams of fat F in an order of h hamburgers, c chicken sandwiches, f orders of fries, and o orders of onion rings.arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning