Explanation Given Information: The flux of radio emission from the sun can be approximated by the model F ( t ) = 49.6 sin [ 0.602 ( t − 1.48 ) ] + 111 where t is number of years since January 1 , 1997 and F ( t ) is the average flux of solar emissions of a specified wavelength at time t. Formula Used: The chain rule is being used which can be represented with the following formula: d d x ( sin u ) = d d x ( sin u ) ⋅ d u d x The following derivative formula is being used: d d x ( sin x ) = cos x Calculation: Consider the function F ( t ) = 49.6 sin [ 0.602 ( t − 1.48 ) ] + 111 . Determine the derivative with respect to t. F ( t ) = 49.6 sin [ 0.602 ( t − 1.48 ) ] + 111 Separate the terms of the derivative function. d d t 49.6 sin [ 0.602 ( t − 1.48 ) ] + d d t ( 111 ) Apply the chain rule. F ′ ( t ) = 49.6 d d t sin [ 0.602 ( t − 1.48 ) ] + 0 F ′ ( t ) = 49

7th Edition

ISBN: 9781337291248

Author: Waner, Stefan.

Publisher: Cengage Learning,

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Chapter 9.2, Problem 60E

To determine

To calculate: The value of F′(5.5) and interpret the result when the flux of radio emission from the sun can be approximated by the model F(t)=49.6sin[0.602(t−1.48)]+111 where t is number of years since January 1,1997 and F(t) is the average flux of solar emissions of a specified wavelength at time t.

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Chapter 9 Solutions

Applied Calculus

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Solution Summary: The author explains how the flux of radio emission from the sun is decreasing with the rate of 22.42 per year since January 1,1997.

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Chapter 9 Solutions