Explanation Given: Perceived Brightness B of a light = k I 2 3 where I is the light intensity, k is a constant Calculation: Step 1: Take the derivative of the perceived brightness with respect to the light intensity d B d I = d ( k I 2 3 ) d I = 2 k 3 I − 1 3 = 2 k 3 I To determine (b) With explanation how adding another pound to a load W is felt more strongly when W is large than when W is small

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Question

Chapter 3.4, Problem 47E

To determine

(a)

With explanation how a 1-unit increase in light intensity is felt more strongly when I is small than when I is large

To determine

(b)

With explanation how adding another pound to a load W is felt more strongly when W is large than when W is small

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Chapter 3.4, Problem 46E

Chapter 3.4, Problem 48E

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According to Stevens’ Law in psychology, the perceived magnitude of a stimulus is proportional(approximately) to a power of the actual intensity I of the stimulus. Experiments show that the perceivedbrightness B of a light satisfies B = kI2/3, where I is the light intensity, whereas the perceived heaviness Hof a weight W satisfies H = kW3/2 (k is a constant that is different in the two cases). Compute dB/dI anddH/dW and state whether they are increasing or decreasing functions. Then explain the following statements: (a) A 1-unit increase in light intensity is felt more strongly when I is small than when I is large.(b) Adding another pound to a load W is felt more strongly when W is large than when W is small.

According to the Stefan-Boltzmann Law, the thermal radiation energy emitted (per unit time) by a hot object is proportional to the fourth power of the absolute temperature: E = kTª, where k is a proportionality constant and T is measured in kelvin. Find the relationship between the measured error in temperature T and the resulting error in energy E.

According to the Stefan-Boltzmann Law, the thermal radiation energy emitted (per unit time) by a hot object is proportional to the fourth power of the absolute temperature: E = kT4, where k is a proportionality constant and T is measured in kelvin. Find the relationship between the measured error in temperature T and the resulting error in energy E.

Chapter 3 Solutions

Calculus - Standalone book

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(a) With explanation how a 1-unit increase in light intensity is felt more strongly when I is small than when I is large

Solution Summary: The author explains how a 1-unit increase in light intensity is felt more strongly when one is small than when the other is large.