Explanation Given information: The basal metabolism (BM) of an organism over a certain time period may be described as the total amount of heat in kilocalories (kcal) that the organism is at rest and not subject to stress. The basal metabolic rate (BMR) is the rate in kcal per hour at which the organism produces heat. The BMR of an animal such as a desert rat fluctuates in response to changes in temperature and other environmental factors. The BMR generally follows a diurnal cycle, rising at night during low temperatures and decreasing during the warmer daytime temperature and B M R ( t ) = 0.4 + 0.2 cos ( π t 12 ) kcal per hour ( t = 0 corresponds to 3 a.m.) as shown in the figure below, Explanation: B M R ( t ) = 0.4 + 0.2 cos ( π t 12 ) kcal per hour is the rate. To find basal metabolism(BM) for 1 day, take integration of BMR from t = 0 to t = 24 ⇒ B M = ∫ 0 24 B M R ( t ) d t = ∫ 0 24 ( 0.4 + 0.2 cos ( π t 12 ) ) d t = ∫ 0 24 0.4 d t + 0.2 ∫ 0 24 cos ( π t 12 ) d t In the second integral, substitute π t 12 = u Differentiating on both sides, π 12 d t = d u ⇒ d t = 12 π d u B M = ∫ 0 24 0

MyLab Math with Pearson eText -- 24 Month Access -- for Calculus & Its Applications

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ISBN: 9780137590469

Author: Larry Goldstein / David Lay

Publisher: Pearson Education (US)

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Chapter 8.3, Problem 48E

To determine

The basal metabolism(BM) of an organism for 1 day, if BMR(t)=0.4+0.2 cos(πt12) kcal per hour, where the basal metabolism(BM) of an organism over a certain time period may be described as the total amount of heat in kilocalories(kcal) that the organism is at rest and not subject to stress.

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Chapter 8.3, Problem 47E

Chapter 8.3, Problem 49E

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Solution Summary: The author explains the basal metabolism of an organism over a certain time period may be described as the total amount of heat in kilocalories that the organism is at rest and not subject to stress.

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The basal metabolism(BM) of an organism for 1 day, if BMR(t)=0.4+0.2 cos(πt12) kcal per hour, where the basal metabolism(BM) of an organism over a certain time period may be described as the total amount of heat in kilocalories(kcal) that the organism is at rest and not subject to stress.

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Chapter 8 Solutions