(a) Explanation Given Information: The rate of sale in t weeks is n ( t ) = 196 + t 2 − 0.16 t 5 copies per week. Formula used: If f(x) and g(x) are two functions then sum and difference rules for an integral is, ∫ [ f ( x ) ± g ( x ) ] d x = ∫ f ( x ) d x ± ∫ g ( x ) d x Constant multiple rule is ∫ k ⋅ f ( x ) d x = k ∫ f ( x ) d x where k is a constant. Power rule for the indefinite integral is ∫ x n d x = x n + 1 n + 1 + C , valid for the condition n ≠ − 1 , where C is the constant of integration . Calculation: Consider that rate of sale in t weeks, N ′ ( t ) = n ( t ) = 196 + t 2 − 0.16 t 5 Also consider that sale in the starting was zero, N ( 0 ) = 0 The total sale N ( t ) is anti-derivative of N ′ ( t ) . N ( t ) = ∫ ( 196 + t 2 − 0.16 t 5 ) d t Apply sum and difference rule. ∫ ( 196 + t 2 − 0.16 t 5 ) d t = ∫ 196 d t + ∫ t 2 d t − ∫ 0.16 t 5 d t Apply constant multiple rule in each term. ∫ 196 d t + ∫ t 2 d t − ∫ 0.16 t 5 d t = 196 ∫ d t + 1 ∫ t 2 d t − 0 (b) To determine To calculate: The total sale of a novel “The secret Loves of John O” N ( t ) in 6 weeks, if the rate of sale in t weeks is n ( t ) = 196 + t 2 − 0.16 t 5 copies per week.

Finite Mathematics and Applied Calculus (MindTap Course List)

7th Edition

ISBN: 9781337274203

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 13, Problem 45RE

(a)

To determine

To calculate: The total sale of a novel “The secret Loves of John O” N(t) with respect to time t, if the rate of sale in t weeks is n(t)=196+t2−0.16t5 copies per week.

(b)

To determine

To calculate: The total sale of a novel “The secret Loves of John O” N(t) in 6 weeks, if the rate of sale in t weeks is n(t)=196+t2−0.16t5 copies per week.

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Chapter 13, Problem 44RE

Chapter 13, Problem 46RE

Chapter 13 Solutions

Finite Mathematics and Applied Calculus (MindTap Course List)

Ch. 13.1 - In Exercises 142, evaluate the integral. [HinT:...Ch. 13.1 - Prob. 2E Ch. 13.1 - Prob. 3E Ch. 13.1 - Prob. 4E Ch. 13.1 - Prob. 5E Ch. 13.1 - Prob. 6E Ch. 13.1 - Prob. 7E Ch. 13.1 - Prob. 8E Ch. 13.1 - Prob. 9E Ch. 13.1 - Prob. 10E

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The total sale of a novel “The secret Loves of John O” N ( t ) with respect to time t, if the rate of sale in t weeks is n ( t ) = 196 + t 2 − 0.16 t 5 copies per week.

Solution Summary: The author calculates the total sale of a novel "The secret Loves of John O" with respect to time t, if the rate of sale is n(t)=196+t