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(g) The graphs of the functions f (t) and g (t), for the domain t 2 0 are shown:

(g) The graphs of the functions f (t) and g (t), for the domain t 2 0 are shown:

Calculus: Early Transcendentals
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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(g) The graphs of the functions f (t) and g (t), for the domain t >0 are shown: 100 g(1) f(r) 15 i. Explain why the domain of the graphs are taken as t 20 ii. In your own words give a plausible explanation as to why the marimum TEF is higher for a lean person than for an obese person and also, why the TEF function of a lean person approaches zero at a faster rate than that of an obese person with respect to time. Finally, draw a conclusion of the efficiency of digestion for a lean person in comparison to that of an obese person.
Transcribed Image Text:(g) The graphs of the functions f (t) and g (t), for the domain t >0 are shown: 100 g(1) f(r) 15 i. Explain why the domain of the graphs are taken as t 20 ii. In your own words give a plausible explanation as to why the marimum TEF is higher for a lean person than for an obese person and also, why the TEF function of a lean person approaches zero at a faster rate than that of an obese person with respect to time. Finally, draw a conclusion of the efficiency of digestion for a lean person in comparison to that of an obese person.
The thermic effect of food (TEF) is the increase in metabolic rate after a meal. To model TEF which is measured in kJ/h, researchers use the following functions: S (t) = 175.9te 9 (t) = 113.6te where f (t) is the TEF for a lean person and g (t) is the TEF for an obese person respectively and t, is the time in hours. Find the marimum value of the TEF for both individuals. Solve the above, by answering the following questions: (a) Examine both functions above and then rewrite the TEF as a single general function h (t) by replacing the numerical constants in f (t) and g (t) with the symbolic constants a and b. (b) Calculate the derivative h' (t). (c) Find the intervals of increase or decrease of h (t). (d) Using your answer found in part (c) above, find the maximum TEF for a lean person and the maximum TEF for an obese person respectively by substituting the appropriate values for a and b. (e) Calculate the derivative h" (t). (f) Using your answer found in part (e) above, find the inflection point for the graph of f (t) (for a lean person) and for the graph of g(t) (for an obese person) respectively and interpret in your own words the physical meaning of this term.
Transcribed Image Text:The thermic effect of food (TEF) is the increase in metabolic rate after a meal. To model TEF which is measured in kJ/h, researchers use the following functions: S (t) = 175.9te 9 (t) = 113.6te where f (t) is the TEF for a lean person and g (t) is the TEF for an obese person respectively and t, is the time in hours. Find the marimum value of the TEF for both individuals. Solve the above, by answering the following questions: (a) Examine both functions above and then rewrite the TEF as a single general function h (t) by replacing the numerical constants in f (t) and g (t) with the symbolic constants a and b. (b) Calculate the derivative h' (t). (c) Find the intervals of increase or decrease of h (t). (d) Using your answer found in part (c) above, find the maximum TEF for a lean person and the maximum TEF for an obese person respectively by substituting the appropriate values for a and b. (e) Calculate the derivative h" (t). (f) Using your answer found in part (e) above, find the inflection point for the graph of f (t) (for a lean person) and for the graph of g(t) (for an obese person) respectively and interpret in your own words the physical meaning of this term.
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