Concept explainers
Reminder Round all answers to two decimal places unless otherwise indicated.
New Construction The following table shows the value
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a. Make a table showing, for each of the
b. Explain in practical terms what
c. Over what period was the growth in value of new construction the greatest?
d. According to the table, in what year was the value of new construction the greatest?
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Chapter 1 Solutions
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Additional Math Textbook Solutions
Intermediate Algebra (12th Edition)
Elementary & Intermediate Algebra
Intermediate Algebra (8th Edition)
College Algebra Essentials
A Graphical Approach to College Algebra (6th Edition)
Glencoe Algebra 2 Student Edition C2014
- Reminder Round all answers to two decimal places unless otherwise indicated. A Coin CollectionThe value of a coin collection increases as new coins are added and the value of some rare coins in the collection increases. The value V, in dollars, of the collection t years after the collection was started is given by the following table. t=time,inyears V=value,indollars 0 130.00 1 156.00 2 187.20 3 224.64 4 269.57 a. Show that these data are exponential. b. Find an exponential model for the data. c. According to the model, when will the collection have a value of 500?arrow_forwardReminder Round all answer to two decimal places unless otherwise indicated. Lean Body Weight in Females This is a continuation of Exercise 20. The text cited in Exercise 20 gives a more complex method of calculating lean body weight for your adult females: L=19.81+0.73W+21.2R0.88A1.39H+2.43F. Here L is lean body weight in pounds, W is weight in pounds, R is wrist diameter in inches, A is abdominal circumference in inches, H is hip circumference in inches, and F is forearm circumference in inches. Assuming the validity of the formulas given here and in Exercise 20, compare the increase in lean body weight of young adult males and of young adult females if their weight increases but all others factors remain the same. Lean Body Weight in Males Your lean body weight L is the amount you would weigh if all the fat in your body were to disappear. One text gives the following estimate of lean body weight L in pounds for young adult males: L=98.42+1.08W4.14A, Where W is total weight in pounds and A is abdominal circumference in inches. 7 a. Consider a group of young adult males who have the same abdominal circumference. If their weight increases but their abdominal circumference remains the same, how does their lean body weight change? b. Consider a group of young adult males who have the same weight. If their abdominal circumference decreases but their weight stays the same, how does their lean body weight change? c. Suppose a young adult male has a lean body weight of 144 pounds. Over a period of time, he gains 15 pounds in total weight, and his abdominal circumference increases by 2 inches. What is his lean body weight now?arrow_forwardReminder Round all answer to two decimal places unless otherwise indicated. Lean Body Weight in Males Your lean body weight L is the amount you would weigh if all the fat in your body were to disappear. One text gives the following estimate of lean body weight L in pounds for young adult males: L=98.42+1.08W4.14A, where W is total weight in pounds and A is abdominal circumference in inches. 7 a. Consider a group of young adult males who have the same abdominal circumference. If their weight increases but their abdominal circumference remains the same, how does their lean body weight change? b. Consider a group of young adult males who have the same weight. If their abdominal circumference decreases but their weight stays the same, how does their lean body weight change? c. Suppose a young adult male has a lean body weight of 144 pounds. Over a period of time, he gains 15 pounds in total weight, and his abdominal circumference increases by 2 inches. What is his lean body weight now?arrow_forward
- Reminder Round all answers to two decimal places unless otherwise indicated. Growth in Weight The following table gives, for a certain man, his weight W=W(t) in pounds at age t in years. t=Age(years) W=Weight pounds 4 36 8 54 12 81 16 128 20 156 24 163 a. Make a table showing, for each of the 4- year periods, the average yearly rate of change in W. b. Describe in general terms how the mans gain in weight varied over time. During which 4-year period did the man gain the most in weight? c. Estimate how much the man weighed at age 30. d. Use the average rate of change to estimate how much he weighed at birth. Is your answer reasonable?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. Yellowfin Tuna Data were collected comparing the weight W, in pounds, of a yellowfin tuna to its length L, in centimeters. These data are presented in the following table. L=Length W=Weight 70 14.3 80 21.5 90 30.8 100 42.5 110 56.8 120 74.1 130 94.7 140 119 160 179 180 256 a. What is the average rate of change, in weight per centimeter of length, in going from a length of 100 centimeters to a length of 110 centimeters? b. What is the average rate of change, in weight per centimeter of length, in going from 160 to 180 centimeters? c. Judging from the data in the table, does an extra centimeter of length make more difference in weight for a small tuna or for a large tuna? d. Use the average rate of change to estimate the weight of a yellowtuna fish that is 167 centimeters long? e. What is the average rate of change, in length per pound of weight, in going from a weight of 179 pounds to a weight of 256 pounds? f. What would you expect to be the length of a yellow tuna weighing 225 pounds?arrow_forward
- Reminder Round all answers to two decimal places unless otherwise indicated. t is measured in thousands of years, and C=C(t) is the amount, in grams, of carbon-14 remaining. Carbon-14 unstable radioactive t=Thousandofyears C=Gramsremaining 0 5 5 2.73 10 1.49 15 0.81 20 0.44 a. What is the average yearly rate of change of carbon-14 during the first 5000 years? b. How many grams of carbon-14 would you expect to find remaining after 1236 years? c. What would you expect to be the limiting value of C?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 decimal places unless otherwise indicated. The Spread of AIDS This table shows the cumulative number N=N(t) of AIDS cases in the United States that have been reported to the Centers for Disease Control and Prevention by the end of the year given. The source for these data, the U.S. Centers for Disease Control and Prevention in Atlanta, cautions that they are subject to retrospective change. a. What does dNdt mean in practical terms? b. From 2010to2014, was dNdt ever negative? t=year N=totalcasereported 2010 1,140,203 2011 1,172,489 2012 1,191,061 2013 1,217,863 2014 1,236,994arrow_forward
- ReminderRound all answers to two decimal places unless otherwise indicated. Deaths from the Heart DiseaseTable A and B show the deaths per 100,000 caused by heart disease in the United States for males and females aged 55 to 64 years. The function Hm gives deaths per 100,000 for males, and Hf gives deaths per 100,000 for females. a.Approximate the value of dHmdt in 2004 using the average rate of change from 2004 to 2007. b.Explain the meaning of the number you calculated in part a in practical terms. You should, among other things, tell what the sign means. TABLE AHeart Disease Deaths per 100,000 for Males Aged 55 to 64 Years t=year Hm=deathsper100,000 1990 537.3 2000 371.7 2003 331.7 2004 312.8 2007 288.8 c.Use your answer from part a to estimate the heart disease death rate for males aged 55 to 64 years in 2006 d.Approximate the value of dHfdt for 2004 using the average rate of change from 2004 to 2007. e.Explain what your calculations from parts a and d tell you about comparing heart disease deaths for men and women in 2004. TABLE BHeart Disease Deaths per 100,000 for Females Aged 55 to 64 Years t=year Hf=deathsper100,000 1990 215.7 2000 159.3 2003 141.9 2004 131.5 2007 117.9arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Arterial Blood Flow Medical evidence shows that a small change in the radius of an artery can indicate a large change in blood flow. For example, if one artery has a radius only 5 larger than another, the blood flow rate is 1.22 times as large. Further information is given in the table below. Increase in radius Times greater blood flow rate 5 1.22 10 1.46 15 1.75 20 2.07 a. Use the average rate of change to estimate how many times greater the blood flow rate is in an artery that has a radius 12 larger than another. b. Explain why if the radius is increased by 12 and then we increase the radius of the new artery by 12 again, the total increase in the radius is 25.44. c. Use parts a and b to answer the following question: How many times greater is the blood flow rate in an artery that 25.44 larger in radius than another? d. Answer the question in part c using the average rate of change.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Population Growth The following table shows the population of reindeer on an island as of the given year. date 1945 1950 1955 1960 population 40 165 678 2793 We let t be the number of years since 1945, so that t=0 corresponds to 1945, and we let N=N(t) denote the population size. a. Approximate dNdt for 1955 using the average rate of change from 1955 to 1960, and explain what this number means in practical terms. b. Use your work from part a to estimate the population in 1957. c. The number you calculated in part a is an approximation to the actual rate of change. As you will be asked to show in the next exercise, the reindeer population growth can be closely modeled by an exponential function. With this in mind, du you think your answer in part a is too large or too small? Explain your reasoning.arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning