Concept explainers
Remainder Round all answers to two decimal places unless otherwise indicated.
Rice production in Asia Improved agricultural practices, including better utilization of fertilizers and use of improved plant varieties, have resulted in increased rice yields in Asia. The accompanying table shows the average yield
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5 | 3.32 |
10 | 3.61 |
15 | 3.73 |
20 | 3.95 |
25 | 4.11 |
a. One study used a linear function to approximate yield as a function of time. Find an approximate linear model for
b. Explain what the slope of the linear model tells you.
c. Use the model to calculate
d. What yield would the model estimate for 2025?
e. The 1993 report of the International Rice Research Institute predicted that rice requirements in Asis would grow exponentially. If the rice requirements in 2025 are 6.44 tons per hectare, will rice production in 2025 meet those requirements?
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Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
- Remainder Round all answers to two decimal places unless otherwise indicated. Energy Cost of Running Physiologists have studied the steady-state oxygen consumption measured per unit of mass in a running animal as a function of its velocity i.e., its speed. They have determined that the relationship is approximately linear, at least over an appropriate range of velocities. The table below gives the velocity v, in kilometres per hour, and the oxygen consumption E, in milliliters of oxygen per gram per hour, for the rhea, a large flightless South American bird. For comparison, 10 kilometers per hour is about 6.2 miles per hour. Velocity v Oxygen Consumption E 2 1.0 5 2.1 10 4.0 12 4.3 a.Find the equation of the regression line for E in terms of v. b.The slope of the linear function giving oxygen consumption in terms of velocity is called the cost of transport for the animal, since it measures the energy required to move a unit mass by 1 unit distance. What is the cost of transport for the rhea? c.Physiologists have determined the general approximate formula C=8.5W-0.40 for the cost of transport C of an animal weighing W grams. If the rhea weighs 22, 000 grams, is its cost of transport from part b higher or lower than what the general formula would predict? Is the rhea a more or a less efficient runner than a typical animal its size? d.What would your equation from part a lead you to estimate for the oxygen consumption of a rhea at rest?arrow_forwardRemainder: Round all answer to two decimal places unless otherwise indicated. a. How much does the stationery alone cost for a 3-page letter? b. How much does it cost to prepare and mail a 3-page letter if your secretary spends 2 hours on typing and corrections? c. Use a formula to express the cost of the stationery alone for a letter as a function of the number of pages in the letter. Identify the function and each of the variables you use, and state the units. d. Use a formula to express the cost of preparing and mailing a letter as a function of the number of pages in the letter and the time it takes your secretary to type it. Identify the function and each of the variables you use, and state the units. e. Use the function you made in part d to find the cost of preparing and mailing a 2-page letter that it takes your secretary 25 minutes to type.arrow_forwardRemainder Round all answers to two decimal places unless otherwise indicated. Running Ants A scientist collected the following data on the speed, in centimeters per second, at which ants ran at the given ambient temperature, in degrees Celsius. Temperature Speed 25.6 2.62 27.5 3.03 30.3 3.57 30.4 3.56 32.2 4.03 33.0 4.17 33.8 4.32 a.Find the equation of the regression line, giving the speed as a function of the temperature. b.Explain in practical terms the meaning of the slope of the regression line. c.Express, using functional notation, the speed at which the ants run when the ambient temperature is 29 degrees Celsius, and then estimate that value. d.The scientist observes the ants running at a speed of 2.5 centimeters per second. What is the ambient temperature?arrow_forward
- Inflation Assuming that the annual rate of inflation averages 4 over the next 10 years, the approximate costs C of goods or services during any year in that decade can be modeled by Ct=P1.04t, where t is the time in years and P is the present cost. The price of an oil change for your car is presently $29.88. Estimate the price 10 years from now.arrow_forwardRemainder Round all answers to two decimal places unless otherwise indicated. Crayola Colors The table below shows the number C of Crayola colors available t years after 1990. t = years since 1990 C = number of colors 3 8 49 48 58 64 72 72 90 80 98 120 103 120 a.Find the equation of the regression line for C as a function of t. b.How many Crayola colors does the regression line indicate for 1993? Round your answer to the nearest whole number. Note that the actual number is 96. c.Plot the data points and the regression line.arrow_forwardReminderRound all answers to two decimal places unless otherwise indicated. River FlowThe graph in Figure 1.37 shows the mean flow F for the Arkansas River, in cubic feet of water per second, as a function of the time t, in months, since the start of the year. The flow is measured near the rivers headwaters in the Rocky Mountains. a.Use functional notation to express the flow at the end of July, and then estimate that value. b.When is the flow at its greatest? c.At what time is the flow increasing the fastest? FIGURE 1.37 Flow for the Arkansas River d.Estimate the average rate of change per month in the flow during the first 2 months of the year. e.In light of the source of the Arkansas River, interpret your answers to parts b, c, and d.arrow_forward
- Remainder Round all answers to two decimal places unless otherwise indicated. Whole Crop Weight Versus Rice Weight A study by Horie compared the dry weight of brown rice B with the dry weight W of the whole crop including stems and roots. These data, in tons per hectare, for the variety Nipponbare grown in various environmental conditions are partially presented in the table below. Whole crop weight W Rice Weight B 6 1.8 11.1 3.2 13.7 3.7 14.9 4.3 17.6 5.2 a.Find an approximate linear model for B as a function of W. b.Which sample might be considered to have a lower rice weight than expected from the whole crop weight? c.How much additional rice weight can be expected from 1 ton per hectare of additional whole crop weight?arrow_forwardTEST YOUR UNDERSTANDING|FOR EXAMPLE 1.3 Use the notion of the example. Explain the meaning of W(1973), and use the average rate of change to estimate its value. Example 1.3 WOMEN EMPLOYED OUTSIDE THE HOME Table 1.2 shows the number W of women in the United States employed outside the home as a function of the date d. It was taken from the Statistical Abstract of the United States TABLE 1.2 Number of Women Employed Outside the Home in the United States d=Year 1970 1980 1990 2000 2010 W=Numberinmillions 31.5 45.5 56.8 66.3 71.9 Part 1 Explain the meaning of W(1970) and give its value. Part 2 Explain the meaning of W(1975) and estimate its value. Part 3 Express the number of women employed outside the home in 1972 in functional notation, and use the average yearly rate of change from 1970 to 1980 to estimate its value. Part 4 According to the 1950 Statistical Abstract of the United States, in 1943 there were 18.7 million women employed outside the home, and in 1946 the number was 16.8 million. On the basis of this information, find the average yearly rate of change in W from 1943 to 1946 and the average decrease per year over this time interval. Use the result to estimate W(1945).arrow_forwardReminder Round all answer to two decimal places unless otherwise indicated. Hair Growth When you are 18 years old you have a hair that is 14 centimeters long, and your hair grows about 12 centimeters each year. Let H(t) be the length, in centimeters, of that hair t years after age 18. a. Find a formula that gives H as a linear function of t. b. How long will it take for the hair to reach a length of 90 centimeters?arrow_forward
- Remainder Round all answers to two decimal places unless otherwise indicated. Long Jump The following table shows the length, in meters, of the winning long jump in the Olympic Games for the indicated year. One meter is 39.37 inches. Year 1900 1904 1908 1912 Length 7.19 7.34 7.48 7.60 a.Find the equation of the regression that gives the length as a function of time. Round the regression line parameters to three decimal places. b.Explain in practical terms the meaning of the slope of the regression line. c.Plot the data points and the regression line. d.Would you expect the regression line formula to be a good model of the winning length over a long period of time? Be sure to explain your reasoning. e.There were no Olympic Games in 1916 because of World War I, but the winning long jump in the 1920 Olympic Games was 7.15 meters. Compare this with the value that the regression line model gives. Is the result consistent with your answer to part d?arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Choosing a Bat A chart from Dicks sporting Goods gives the recommended bat length B in inches for a man weighing between 161 and 170 pounds as a function of his height h in inches. The table is partially reproduced on the next page. h=Height B=Batlength 4548 30 4952 31 5356 31 5760 32 6164 32 6568 33 6972 33 73+ 33 a. Explain in practical terms the meaning of B(55) and give its value. b. Use functional notation to express the recommended bat length for a man weighing between 161 and 170 pounds if his height is 63inches.arrow_forwardRemainder Round all answers to two decimal places otherwise indicated. College Enrollment This is a continuation of Exercise 9. We use the data in the college enrolment table that appears in Exercise 9. a.Find the equation of the regression line model for college enrolment as a function of time, and add its graph to the data plot made in Exercise 9. b.Explain the meaning of the slope of the line you found in part a. c.Express, using functional notation, the enrolment in American private colleges in2010, and then estimate that value. d.Enrollment in American private colleges in 2013 was 5.74 million. Does it appear that the trend established in the mid-2000s was valid in 2013?arrow_forward
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