. Program Explanation Given information: The population function P satisfies the differential equation d P d t = ( k + b cos 2 π t ) P . Here, t is in years. k and b are positive constants. The growth rate function is r ( t ) = k + b cos 2 π t . The initial value population is P 0 . Explanation: Solve the differential equation d P d t = ( k + b cos 2 π t ) P as follows: d P P = ( k + b cos 2 π t ) d t ∫ d P P = ∫ ( k + b cos 2 π t ) d t ln P = k t + b 2 π sin 2 π t + ln C Substitute, P ( t = 0 ) = P 0 in the above equation and solve for arbitrary constant C. ln P 0 = ln C P 0 = C Therefore, the particular solution for the differential equation d P d t = ( k + b cos 2 π t ) P is simplified as, ln P = k t + b 2 π sin 2 <

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Strongly Connected Components

A directed graph in which a path exists between all its pairs of vertices is called a strongly connected graph. A portion of the strongly connected directed graph that contains a path to reach from each vertex to other vertices is called a strongly conne…

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Chapter 2.1, Problem 39P

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Program Description: Purpose ofthe problem is to construct a graph that represent the difference in growth of population function for same initial population but different growth rate.

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Chapter 2.1, Problem 38P

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Program Description: Purpose ofthe problem is to construct a graph that represent the difference in growth of population function for same initial population but different growth rate.

Solution Summary: The author explains how to construct a graph that represents the difference in growth of population function for same initial population but different growth rate.

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Program Description: Purpose ofthe problem is to construct a graph that represent the difference in growth of population function for same initial population but different growth rate.

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Chapter 2 Solutions