Concept explainers
Harris-Benedict Formula Your basal metabolic rate is the amount of energy (in calories) your body needs to function at rest. The Harris-Benedict formula is used to estimate the basal metabolic rate. There is one formula for adult males and another for adult females. In these formulas, w is your body weight in pounds, h is your height in inches, a is your age in years,
Use functional notation to express your own basal metabolic rate, and then calculate its value.
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Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
- Air Temperature As dry air moves upward, it expand and, in so doing, cools at a rate of about 1°C for each 100-meter rise, up to about 12 km. (a) If the ground temperature is 20°C, write a formula for the temperature at height h. (b) What range of temperatures can be expected if an air plane lakes off and reaches a maximum height of 5 km?arrow_forwardAlexanders Formula One interesting problem in the study of dinosaurs is to determine from their tracks how fast they ran. The scientist R. McNeil Alexander developed a formula giving the velocity of any running animal in terms of its stride length and the height of its hip above the ground. The stride length of dinosaur can be measured from successive prints of the same foot, and the hip height roughly the leg length can be estimated on the basis of the size of a footprint, so Alexanders formula gives a way of estimating from dinosaur tracks how fast the dinosaur was running. See Figure 2.45. If the velocity v is measured in meters per second, and the stride length s and hip height h are measured in meters, then Alexanders formula is v=0.78s1.67h1.17. For comparison, a length of 1 meter is 39.37inches, and a velocity of 1 meter per second is about 2.2milesperhour. First, we study animals with varying stride lengths, but all with a hip height of 2meters so h=2 i. Find the formula for the velocity v as a function of the stride length s. ii. Make a graph of v versus s. Include stride lengths from 2to10meters. iii. What happens to the velocity as the stride length increases? Explain your answer in practical terms. iv. Some dinosaur tracks show a stride length of 3meters, and a scientist estimates that the hip height of the dinosaur was 2meters. How fast was the dinosaur running?arrow_forwardEnlarging a Field A farmer has a rectangular cow pasture with width 100 ft. and length 180 ft. An increase the number of requires the farmer to increase the area of her pasture. She has two options: Option 1: Increase the length of the field. 0ption 2: Increase the width at the field. It costs $10 per foot to install new fence. Moving the old fence costs $6 per linear foot of fence to be moved. (a) For each option, find a formula for A, the area gained, in terms of the cost C. (b) Complete the table for the area gained in terms of the cost for each option. (c) If the farmer has $1200 for this project, which option gives her the greatest gain in area for her money? What if she had $2000 for the project?arrow_forward
- pH of Saliva The pH of saliva is normally in the range of 6.4 to 7.0. However, when a person is ill, the persons saliva becomes more acidic. a When Marco is sick, he tests the pH of his saliva and finds that it is 5.5. What is the hydrogen ion concentration of his saliva? b Will the hydrogen ion concentration in Marcos saliva increase or decrease as he gets better? c After Marco recovers, he tests the pH of his saliva, and it is 6.5. Was the saliva more acidic or less acidic when he was sick?arrow_forwardFalling-Body Problems Suppose an object t dropped from a height h0 above the ground. Then its height after t seconds is given by h=16t2+h0 , where h ¡s measured in feet. Use this information Lo solve the problem. If a ball is dropped from 288 ft above the ground, how bug does it take to reach ground level?arrow_forwardThe Beer-Lambert Law As sunlight passes through the waters of lakes and oceans, the light is absorbed, and the deeper it penetrates, the more its intensity diminishes. The light intensity I at depth x is given by the Beer-Lambert Law: I=I0ekx where I0 is the light intensity at the surface and k is a constant that depends on the murkiness of the water see page 402. A biologist uses a photometer to investigate light penetration in a northern lake, obtaining the data in the table. Light intensity decreases exponentially with depth. Use a graphing calculator to find an exponential function of the form given by the Beer-Lambert Law to model these data. What is the light intensity I0 at the surface on this day, and what is the murkiness constant k for this lake? Hint: If your calculator gives you a function of the form I=abx, convert this to the form you want using the identities bx=eln(bx)=exlnb. See Example 1b. Make a scatter plot of the data, and graph the function that you found in part a on your scatter plot. If the light intensity drops below 0.15 lumen lm, a certain species of algae cant survive because photosynthesis is impossible. Use your model from part a to determine the depth below which there is insufficient light to support this algae. Depth ft Light intensity lm Depth ft Light intensity lm 5 10 15 20 13.0 7.6 4.5 2.7 25 30 35 40 1.8 1.1 0.5 0.3arrow_forward
- Adult Weight from Puppy Weight There is a formula that estimates how much your puppy will weigh when it reaches adulthood. The method we present applies to medium-seized breeds. First, find your puppys weight w at an age of a weeks, where a is 16 weeks or less. Then the predicted adult weight W=Wa,w, in pounds, is given by the formula W=52wa In this exercises, we consider puppies that weigh w=5 pounds at age a. a. Write a formula for W as a function of the age a. b. Make a graph of W for ages up to 16 weeks. c. Does a weight of 5 pounds at an early age indicate a larger or smaller adult weight than a weight of 5 pounds at a later age? d. Is the graph concave up or concave down? Explain the meaning of the concavity in practical terms.arrow_forwardFish Population The fish population in a certain lake rises and falls according to the formula F=1000(30+17tt2) Here F is the number of fish at time t, where t is measured it years since January 1, 2002, when the fish population was first estimated. On what date will the fish population again be the same as it was on January 1, 2002? By what date will all the fish in the lake have died?arrow_forwardBouncing Ball A ball is dropped from a height of 80 ft. The elasticity of this ball is such that it rebounds three-fourths of the distance it has fallen. How high does the ball rebound on the fifth bounce? Find a formula for how high the ball rebounds on the nth bounce.arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
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