Concept explainers
Reminder Round all answers to two decimal places unless otherwise indicated.
Mosteller Formula for Body Surface Area Body surface area is an important piece of medical information because it is a factor in temperature regulation as well as some drug level determinations. The Mosteller formula gives one way of estimating body surface area
a. Use the Mosteller formula to estimate the body surface area for a man who is
b. The weight of an adult increases by
Want to see the full answer?
Check out a sample textbook solutionChapter 5 Solutions
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
- ReminderRound all answers to two decimal places unless otherwise indicated. DensityThe total weight of a rock depends on its size and is proportional to its density. In this context, density is the weight per cubic inch. Let w denote the weight of the rock in pounds, s the size of the rock in cubic inches, and d the density of the rock in pounds per cubic inch. a. What is the total weight of a 3-cubic-inch rock that weighs 2 pounds per cubic inch? b. Write an equation that shows the proportionality relation. What is the constant of proportionality? c. Use the equation you found in part b to find the total weight of a 14-cubic-inch rock with density 0.3 pound per cubic inch.arrow_forwardReminderRound all answers to two decimal places unless otherwise indicated. Skirt LengthOne authors analyzed skirt lengths in the United Kingdom UK and Germany. To get a standardized measure of skirt length, she calculated the ratio. LengthfromshouldertoskirthemLengthfromshouldertoankle The article includes the following graph of the ratio for skirt length in terms of the year. In the graph, the solid line is the ratio in the UK, and the dashed line is the ratio in Germany. FIGURE 1.32 Ratio for skirt length a.Does a larger ratio indicate a longer or a shorter skirt? b.When were skirt lengths shortest in the UK? c.In this period, did skirt lengths in either Germany or the UK ever reach to the ankle?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 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. 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_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
- ReminderRound all answers to two decimal places unless otherwise indicated. Minimum WageOn July 24, 2008, the federal minimum wage was 6.55perhour. On July 24, 2009, this wage was raised to 7.25perhour. If W(t) denotes the minimum wage, in dollars per hour, as function of time, in years, use the given information to estimate dWdt in 2009.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Estimating Wave Height Sailors use the following function to estimate wave height h, in feet, from wind speed w, in miles per hour h=0.02w2 a. Make a graph of wave height versus wind speed. Include wind speeds of up to 25 miles per hour. b. A small boat can sail safely provided wave heights are no more than 4 feet. What range of wind speed will give safe sailing for this boat?arrow_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_forward
- Reminder Round all answers to two decimal places unless otherwise indicated. Market Supply and demand The quality of wheat, in billions of bushels, that wheat suppliers are willing to produce in a year and offer for sale is called the quantity supplied and is denoted by S. The quantity supplied and is determined by the price P of wheat, in dollars per bushel, and the relation is P=2.13S0.75. The quantity of wheat, in billions of bushels, that wheat consumers are willing to purchase in a year is called the quantity demanded and is denoted by D. The quantity demanded is also determined by the price P of wheat, and the relation is P=2.650.55D. At the equilibrium price, the quality supplied and the quality demanded are the same. Find the equilibrium price for wheat.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Giants Ants and Spiders Many science fiction movies feature animals such as ants, spiders, or apes growing to monstrous sizes and threatening defenseless Earthlings. Of course, they are in the end defeated by the hero and heroine. biologists use power function as a rough guide to relate body weight and cross-sectional area of limbs to length or height. Generally, weight is thought to be proportional to the cube of length, whereas the cross-sectional area of limbs is proportional to the square of length. Suppose an ant, having been exposed radiation is enlarged to 500 times its normal length. Such an event can occur only in Hollywood fantasy. Radiation is utterly incapable of causing such a reaction. a.By how much will its weight be increased? b.By how much will the cross-sectional area of its legs be increased? c.Pressure on a limb is weight divided by cross-sectional area. By how much has the pressure on a leg of the giant ant increased? What do you think is likely to happen to this unfortunate ant? Note: The factor by which pressure increases is given by . FactorofincreaseinweightFactorofincreaseinarea)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. The height of the winning pole vault in the early years of the modern Olympic Games can be modeled as a function of time by the formula H=0.05t+3.3 Here t is the number of years since 1900, and H is the winning height in meters. One meter is 39.37 inches. a. Calculate H(4) and explain in practical terms what your answer means. b. By how much did the height of the winning pole vault increase from 1900 to 1904? From 1904 to 1908?arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning