Kleiber's Law states that the metabolic needs (such as calorierequirements) of a mammal are proportional to its body weight raisedto the 0.75 power.¹ Surprisingly, the daily diets of mammals conformto this relation well. Assuming Kleiber's Law holds, answer thefollowing questions.(a) Write a formula for C, daily calorie consumption, as a function ofbody weight, W.NOTE: Use k for the constant of proportionality.C(W) =(b) If a human weighing 150 pounds needs to consume 1800 caloriesa day, estimate the daily calorie requirement of a horse weighing740 lbs and of a rabbit weighing 11 lbs.NOTE: Round your answers to the nearest calorie.Daily calorie requirement of a horse =Daily calorie requirement of a rabbit =caloriesChoose onecalories(c) On a per-pound basis, which animal requires more calories:a mouse or an elephant?¹S. Strogatz. "Math and the City." The New York Times. May 20, 2009. Kleiber originally

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Answered: as calorie Kleiber's Law states that…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Consider two populations that can be modeled by the logistic equation with the same carrying capacity, but with different values of k. Which population approaches the carrying capacity most quickly, the one with the smaller or larger value of k? You may want to think geometrically (check out some slope fields), analytically (look at the form of the solution), or num into the solution). erically (plug some t values
A new town was incorporated in 1960. The size of the town's population was recorded every 5 years after 1960. Using the variables x, for number of years since 1960, and y, for the size of the population, three models were created to predict the population from the number of years since 1960.
Pierce (1948) mechanically measured the frequency (the number of wing vibrations per second) of chirps (or pulses of sound) made by a striped ground cricket, at various ground temperatures. Since crickets are ectotherms (cold-blooded), the rate of their philosophical processes and their overall metabolism are influenced by temperature. Consequently, there is a reason to believe that temperature would have a profound affect on aspects of their behavior, such as chirp frequency. In general, it was found that crickets did not sing at temperatures colder than 60°F or warmer than 100°F. In the following data let X= chirps/sec for the striped ground cricket and Y= temperature in degrees of Fahrenheit. X 19 19.8 18.4 17.1 15.5 14.7 17.1 15.4 16.2 15 17.2 16 17 14.4 Y 71.6 93.3 84.3 80.6 75.2 69.7 82 69.4 83.3 79.6 82.6 80.6 83.5 76.3 n=14; sigma X; sigma y; sigma x2; (sigma x)2; sigma xy; xbar…
) Two chemicals A and B are combined to form a chemical C. The rate of the reaction is proportional to the product of the instantaneous amounts of A and B not converted to chemical C. Initially there are 43 grams of A and 10 grams of B, and for each gram of B, 1.6 grams of A is used. It has been observed that 13.25 grams of C is formed in 5 minutes. How much is formed in 40 minutes? What is the limiting amount of C after a long time ? grams of C are formed in 40 minutes grams is the limiting amount of C after a long time
Pierce (1948) mechanically measured the frequency (the number of wing vibrations per second) of chirps (or pulses of sound) made by a striped ground cricket, at various ground temperatures. Since crickets are ectotherms (cold-blooded), the rate of their philosophical processes and their overall metabolism are influenced by temperature. Consequently, there is a reason to believe that temperature would have a profound affect on aspects of their behavior, such as chirp frequency. In general, it was found that crickets did not sing at temperatures colder than 60°F or warmer than 100°F. In the following data let X= chirps/sec for the striped ground cricket and Y= temperature in degrees of Fahrenheit. X 19 19.8 18.4 17.1 15.5 14.7 17.1 15.4 16.2 15 17.2 16 17 14.4 Y 71.6 93.3 84.3 80.6 75.2 69.7 82 69.4 83.3 79.6 82.6 80.6 83.5 76.3 n=14; sigma X; sigma y; sigma x2; (sigma x)2; sigma xy; xbar…
A population of fish is living in an environment with limited resources. This environment can only support the population if it contains no more than M fish (otherwise some fish would starve due to an inadequate supply of food, etc.). There is considerable evidence to support the theory that, for some fish species, there is a minimum population m such that the species will become extinct if the size of the population falls below m. Such a population can be modelled using a modified logistic equation: dP =(1-)(-) m dt M
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A population of fish is living in an environment with limited resources. This environment can only support the population if it contains no more than M fish (otherwise some fish would starve due to an inadequate supply of food, etc.). There is considerable evidence to support the theory that, for some fish species, there is a minimum population m such that the species will become extinct if the size of the population falls below m. Such a population can be modelled using a modified logistic equation: dP =(1-)(-) m dt M
Question 2 A patient takes d mg of medicine every 8 hours. Every 8 hours, 80% of the medicine in the patient's bloodstream is eliminated. The medicine has side effects if there is ever 15 mg or more in the patient's blood, but there needs to be at least 2 mg in the patient's blood for it to be effective. (a) What is the maximum safe value for d? (Hint: Consider An, the amount of medicine in the patient's blood immediately after taking the nth dose, and think about what must be true about An to ensure a safe dosing schedule. Write out very carefully what A1, A2, A3 are before trying to find a pattern for An.) (b) What is the minimum effective value for d? (Hint: Consider Bn, the amount of medicine in the patient's blood immediately before taking the nth dose.)

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as calorie Kleiber's Law states that the metabolic needs (such