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# Calorie Consumption Problem: The number of calories an animal must consume per day

ISBN: 9781559533911 468

## Solution for problem 7 Chapter 8-4

Precalculus with Trigonometry: Concepts and Applications | 1st Edition

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Problem 7

Calorie Consumption Problem: The number of calories an animal must consume per day increases with its body mass. However, the number of calories per kilogram of body mass decreases with mass because larger animals have a lower surface-to-volume ratio. On page 130 of Studies in Mathematics, Volume XX, published by Yale University Press (1972), Max Bell reports these data for various mammals: Guinea pig 0.7 223 Rabbit 2 58 Human 70 33 Horse 600 22 Elephant 4000 13 a. Make a scatter plot of the data. Explain why the scatter plot does not tell you very much about the relationship between the variables. Then transform the data by taking the logarithm of the mass and the logarithm of the calorie consumption per kilogram. Run a linear regression on the transformed data and plot it on the same screen as a scatter plot of log (cal/kg) versus log (mass). b. By transforming the equation in part a, show that the calorie consumption is a power function of mass. By running power regression on the original data, show that you get the same power function. c. The smallest mammal is the shrew. Predict the calorie consumption per kilogram for a 2-g shrew. (The need to eat so much compared to body mass is probably why shrews are so mean!) d. In the referenced article, Bell reports that a 150,000-kg whale consumes about 1.7 cal/kg. What does the power function predict for the calories per kilogram if you extrapolate it to the mass of a whale? By what percentage does the answer differ from the given 1.7 cal/kg? Think of a reason why the predicted value is so far from the reported value.

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##### ISBN: 9781559533911

The answer to “Calorie Consumption Problem: The number of calories an animal must consume per day increases with its body mass. However, the number of calories per kilogram of body mass decreases with mass because larger animals have a lower surface-to-volume ratio. On page 130 of Studies in Mathematics, Volume XX, published by Yale University Press (1972), Max Bell reports these data for various mammals: Guinea pig 0.7 223 Rabbit 2 58 Human 70 33 Horse 600 22 Elephant 4000 13 a. Make a scatter plot of the data. Explain why the scatter plot does not tell you very much about the relationship between the variables. Then transform the data by taking the logarithm of the mass and the logarithm of the calorie consumption per kilogram. Run a linear regression on the transformed data and plot it on the same screen as a scatter plot of log (cal/kg) versus log (mass). b. By transforming the equation in part a, show that the calorie consumption is a power function of mass. By running power regression on the original data, show that you get the same power function. c. The smallest mammal is the shrew. Predict the calorie consumption per kilogram for a 2-g shrew. (The need to eat so much compared to body mass is probably why shrews are so mean!) d. In the referenced article, Bell reports that a 150,000-kg whale consumes about 1.7 cal/kg. What does the power function predict for the calories per kilogram if you extrapolate it to the mass of a whale? By what percentage does the answer differ from the given 1.7 cal/kg? Think of a reason why the predicted value is so far from the reported value.” is broken down into a number of easy to follow steps, and 280 words. This full solution covers the following key subjects: . This expansive textbook survival guide covers 106 chapters, and 2321 solutions. Precalculus with Trigonometry: Concepts and Applications was written by and is associated to the ISBN: 9781559533911. The full step-by-step solution to problem: 7 from chapter: 8-4 was answered by , our top Calculus solution expert on 03/16/18, 04:16PM. Since the solution to 7 from 8-4 chapter was answered, more than 211 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Precalculus with Trigonometry: Concepts and Applications, edition: 1.

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