Explanation Given information: The number of mosquitoes is increasing at an estimated rate of ( 2 , 200 + 10 e 0.8 t ) per week. Time t is measured in weeks. Calculation: Show the increasing rate of mosquitoes as follows: n ′ ( t ) = 2 , 200 + 10 e 0.8 t Apply Net change Theorem as follows: The integral of a rate of change is the net change ∫ a b F ′ ( x ) d x = F ( b ) − F ( a ) (1) Here, the lower limit is a and the upper limit is b . Apply Net Change Theorem to calculate the number of mosquito population increase between fifth and ninth weeks of summer. Modify Equation (1) for the calculation of capital number of mosquito population increase. ∫ a b n ′ ( t ) d t = n ( b ) − n ( a ) (2) Substitute 9 for b , 5 for a , and ( 2 , 200 + 10 e 0.8 t ) for n ′ ( t ) in Equation (2)

8th Edition

ISBN: 9781285741550

Author: James Stewart

Publisher: Cengage Learning

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Chapter 8.4, Problem 18E

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To calculate: increased mosquito population during fifth and ninth weeks of summer.

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Chapter 8.4, Problem 17E

Chapter 8.4, Problem 19E

Chapter 8 Solutions

Calculus: Early Transcendentals

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