Concept explainers
Reminder Round all answers to two decimal places unless otherwise indicated.
Note Some of the formulas below use the special number
Yield Response to Several Growth Factors This 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
a. Express using functional notation the percentage of maximum yield produced from
b. One baule of nitrogen is
23. Mitscherlich’s Equation An 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
Here
a. Verify that the formula predicts that
b. Use functional notation to express the percentage of maximum yield produced by
c. The exact value of a baule depends on the nutrient in question. For nitrogen,
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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. Note Some of the formulas below use the special number e, which was presented in the Prologue. 10.Flushing Chlorine City water, which is slightly chlorinated, is being used to flush a tank of heavily chlorinated water. The concentration C=C(t) of chlorine in the tank t hours after flushing begins is given by C=0.1+2.78e0.37tmilligramspergallon 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.arrow_forward
- Reminder 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_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_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
- Reminder Round all answers to two decimal places unless otherwise indicated. Boron Uptake Many factors influence a plants uptake of boron from the soil, but one key factor is soil type. One experiment40 compared plant content C of boron, in parts per million, with the amount B, in parts per million, of water-soluble boron in the soil. In Decatur silty clay, the relation is given by C=33.78+37.5B. In Hartsells fine sandy loam, the relation is given by C=31.22+71.17B. a. What amount of available water-soluble boron will result in the same plant content of boron for Decatur silty clay and Hartsells fine sandy loam? If you choose to solve this problem graphically, we suggest a horizontal span of 0 to 0.5 for B b. For available boron amounts larger than that found in part a, which of the two soil types results in the larger plant content of boron?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. The Photic Zone This is a continuation of Exercise 18. In the ocean, the photic zone is the region where there is sufficient light for photosynthesis to occur. See Figure 4.12. For marine phytoplankton, the photic zone extends from the surface of the ocean to a depth where the light intensity is about 1 of surface light. Near Cape Cod, Massachusetts, the depth of the photic zone is about 16meters. In waters near Cape Cod, by what percentage does light intensity decrease for each additional meter of depth?arrow_forward
- Reminder 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. Competition Between Populations In this exercise, we consider the problem of competition between two populations that vie for resources but do not prey on each other. Let m be the size of the first population, let n be the size of the second both measured in thousands of animals, and assume that the populations coexist eventually. An example of one common model for the intersection is Per capita growth rate for m is 3(1mn) Per capita growth rate for n is 2(10.7m1.1n) At an equilibrium point, the per capita growth rates for m and for n are both zero. If the populations reach such a point, then they will continue at that size indefinitely. Find the equilibrium point in the example above.arrow_forwardReminderRound all answers to two decimal places unless otherwise indicated. Protein Content of Wheat GrainProtein content of wheat grain is affected by soil moisture and the amount of available nitrogen among other things. Figure 1.45 shows" the percent of protein content of wheat grain versus pounds of nitrogen per acre applied in three separate situations. In each case, soil moisture refers to moisture at the soil depth of 2 inches to 12 inches. Situation 1: Irrigation was used when soil moisture dropped to 49. Situation 2: Irrigation was used when soil moisture dropped to 34. Situation 3: Irrigation was used when soil moisture dropped to 1. a. If irrigation begins when soil moisture reaches 49, what application of nitrogen will result in the lowest percentage of protein in wheat grain? b. If irrigation begins when soil moisture reaches 34, what application of nitrogen will result in the same protein content of wheat grain as beginning irrigation when soil moisture reaches 1? c. If you irrigate when soil moisture reaches 34, how much nitrogen should you apply to achieve a 13 protein content in wheat grain? d. Does Figure 1.45 indicate that, for nitrogen levels at 45 pounds per acre or higher, increased protein content in wheat grain is associated with higher or lower soil moisture? FIGURE 1.45 Protein content versus availability of nitrogenarrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning