Explanation Given information: The table shows the monthly change in water stored in Lake Sonoma, California, from March through November 2014. The change is measured in acre-feet per month. On March 1, the water stored was 182,566 acre-feet. S ( t ) be the total water in acre-feet, stored in month t, where t = 0 is March. Month Mar Apr May June July Change in water 3003 − 5631 − 8168 − 8620 − 8270 Month Aug Sept Oct Nov Change in water − 7489 − 6245 − 4593 54,743 Formula used: For a continuous function f ( t ) , a ≤ t ≤ b , the left-hand and right-hand sums are given by Left-hand sum = f ( t 0 ) Δ t + f ( t 1 ) Δ t + ... + f ( t n − 1 ) Δ t Right-hand sum = f ( t 1 ) Δ t + f ( t 2 ) Δ t + ... + f ( t n ) Δ t Where Δ t = b − a n For a continuous function F ' ( t ) , a ≤ t ≤ b , then the fundamental theorem of calculus gives F ( b ) − F ( a ) = ∫ a b F ' ( t ) d t Calculation: On March 1, the water stored was 182,566 acre-feet. ⇒ S ( 0 ) = 182 , 566 The given table can be written as t 0 1 2 3 4 S’(t) 3003 − 5631 − 8168 − 8620 − 8270 t Aug Sept Oct Nov S’(t) − 7489 − 6245 − 4593 54,743 By fundamental theorem of calculus, for the continuous function S ' ( t ) , 0 ≤ t ≤ 3 , we have S ( 3 ) − S ( 0 ) = ∫ 0 3 S ' ( t ) d t To determine (b) To find: The month where the maximum and minimum values of S ( t ) occur. To determine (c) To find: The month where S ( t ) appear to have inflection points.

Applied Calculus, 6e WileyPLUS + Loose-leaf

6th Edition

ISBN: 9781119408901

Author: Deborah Hughes-Hallett, Andrew M. Gleason, Patti Frazer Lock, Daniel E. Flath

Publisher: Wiley (WileyPLUS Products)

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Question

Chapter 6.1, Problem 24P

To determine

(a)

To find and interpret:

S(0) and S(3).

To determine

(b)

To find:

The month where the maximum and minimum values of S(t) occur.

To determine

(c)

To find:

The month where S(t) appear to have inflection points.

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Chapter 6.1, Problem 23P

Chapter 6.1, Problem 25P

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Chapter 6 Solutions

Applied Calculus, 6e WileyPLUS + Loose-leaf

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