Program Explanation Given information: The rate of change of rabbit population P with respect to the time is proportional to the square root of P . The rabbit population is 100 at time t = 0 and the initial condition is d p d t = 20 at t = 0 . Calculation: It is given that the rate of change of rabbit population P with respect to the time is proportional to the square root of P . It can be mathematically expressed as, d p d t ∝ P d p d t = k P Now solve the differential equation d p d t = k P with the separationof the variable as, d p d t = k P d p P = k d t Now integrate the differential equation on both sides. ∫ d p P = ∫ k d t 2 P = k t + c It is given that the rabbit population is 100 at time t = 0 . Now apply the given initial condition P ( 0 ) = 100 on the solution of the differential equation. 2 100 = k ( 0 ) + c 2 100 = c 20 = c Now substitute 20 for c in the solution of the differential equation 2 P = k t + c

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ISBN: 9780135904206

Author: Edwards

Publisher: PEARSON

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A naïve solution for the above-stated problem is to evaluate all of the possible combinations of different pieces of varying size to find the maximum revenue-generating combination. Although this method seems the easiest and quick to practice, it has exp…

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Chapter 2.1, Problem 9P

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Program Description: Purpose of the problem is to find the number of rabbit after one year.

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Chapter 2.1, Problem 8P

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Program Description: Purpose of the problem is to find the number of rabbit after one year.

Solution Summary: The author explains that the rate of change of rabbit population is proportional to the square root of P.

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Program Description: Purpose of the problem is to find the number of rabbit after one year.

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Chapter 2 Solutions