Concept explainers
Reminder Round all answers to two decimal places unless otherwise indicated.
Sales Income The following table shows the net monthly income
|
|
|
|
|
|
|
|
|
|
a. Make a table showing, for each of the intervals in the tax table above, the average rate of change in
b. Use the average rate of change to estimate the net monthly income for monthly real estate sales of
c. Would you expect
Want to see the full answer?
Check out a sample textbook solutionChapter 1 Solutions
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
- Reminder Round all answers to two decimal places unless otherwise indicated. Defense SpendingData about recent federal defense spending are given in the accompanying Statistical Abstract of the United States table. Here t denotes the time, in years, since 1990 and D denotes federal defense spending, in billions of dollars. a.Calculate the average yearly rate of change in defense spending from 1990 to 1995. b.Use your answer from part a to estimate D(3), and explain what it means. t= Years since 1990 D= Spending billions of dollars 0 328.4 5 310.0 10 341.5 15 565.5 20 843.8 c.Calculate the average yearly rate of change in defense spending from 2005 to 2010. d.Use your answer form part c to estimate the value of D(22).arrow_forwardReminder 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. Tax Owed The following table shows the income tax T owed in a certain state as a function of the taxable income I, both measured in dollars. I=Taxableincome T=Taxowed 16,000 870 16,200 888 16,400 906 16,600 924 a. Make a table showing, for each of the intervals in the tax table above, the average rate of change in T. b. Describe the general trend in the average rate of change. What does this mean in practical terms? c. Would you expect T to have a limiting value? Be sure to explain your reasoning.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. 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_forwardReminderRound 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_forward
- Reminder Round all answers to two decimal places unless otherwise indicated. New Construction The following table shows the value B, in billions of dollars, of new construction put in place in the United States during the year t. t=Year B=Value billions of dollars 2000 831.1 2003 891.5 2006 1167.6 2009 935.6 a. Make a table showing, for each of the 3-year periods, the average yearly rate of change in B. b. Explain in practical terms what B(2008) means, and estimate its value. 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?arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Sales Growth A study of the sales s, in thousands of dollars, of a product as a function of time t, in years, yields the equation of change dsdt=0.3s(4s). This is valid for s less than 5. a.What level of sales will be attained in the long run? b.What is the largest rate of growth in sales?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
- Reminder 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_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_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_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning