Explanation Given information: The objective is to find the number of acres covered 24 hours later when the fire is growing at a rate of 8 t acres per hour. Also at t = 0 , the forest fire covers 2000 acres. Concept used: Calculate the change in number of acres using fundamental theorem of calculus. ∫ a b f ( t ) d t = F ( b ) − F ( a ) Calculation: Here, f ( t ) = 8 t , a = 0 and b = 24 The number of acres the fire covers after 24 hours is the original number of acres plus the change, so Acres after 24 hours = 2000 + ∫ 0 24 8 t d t The change in the number of acres is the integral of the rate of change. Change in number of acres = ∫ 0 24 ( 8 t ) d t = [ 8 ( t 1 2 + 1 1 2 + 1 ) ] 0 24 = [ 8 × 2 3 t 2 3 ] 0 24

6th Edition

ISBN: 9781119275565

Author: Hughes-Hallett

Publisher: WILEY

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Chapter 5.4, Problem 17P

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To find the number of acres covered 24 hours later when the fire is growing at a rate of 8t acres per hour.

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Chapter 5.4, Problem 16P

Chapter 5.4, Problem 18P

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To find the number of acres covered 24 hours later when the fire is growing at a rate of 8 t acres per hour.

Solution Summary: The author calculates the change in the number of acres using the fundamental theorem of calculus.

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To find the number of acres covered 24 hours later when the fire is growing at a rate of 8t acres per hour.

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Chapter 5 Solutions