Explanation Given: The rate of increase of population is proportional to the number of people present at time t , the initial population has doubled in 5 years and the initial population is P 0 . Procedure used: (1) Form a differential equation. (2) Integrate the differential equation. (3) Apply initial conditions. Calculation: Form the differential equation from the given information. d P d t = k P d P P = k d t (1) Here, the population is P , the constant is k and the time is t . Integrate equation (1). ∫ d P P = ∫ k d t ln P = k t + c P = e k t e c (2) Substitute P 0 for P and 0 for t in equation (2). P 0 = e k ⋅ 0 e c P 0 = e c Substitute P 0 for e c in equation (2). P = P 0 e k t (3) Substitute 2 P 0 for P and 5 for t in equation (3)

6th Edition

ISBN: 9781284127003

Author: ZILL

Publisher: JONES+BARTLETT LEARNING,LLC (CC)

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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Chapter 2.7, Problem 1E

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Determine the time required for the population to triple and the time required for the population to quadruple.

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Chapter 2.6, Problem 10E

Chapter 2.7, Problem 2E

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4. 5. 6. Let X be a set and let f: XX be a function. We say that f is an involution if fof idx and that f is idempotent if f f = f. (a) If f is an involution, must it be invertible? Why or why not?2 (b) If f is idempotent, must it be invertible? Why or why not? (c) If f is idempotent and x E range(f), prove that f(x) = x. Prove that [log3 536] 5. You proof must be verifiable by someone who does not have access to a scientific calculator or a logarithm table (you cannot use log3 536≈ 5.7). Define the sequence {a} by a = 2-i for i≥ 1. (a) Give the first five terms of the sequence. (b) Prove that the sequence is increasing.

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Chapter 2 Solutions

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Determine the time required for the population to triple and the time required for the population to quadruple.

Solution Summary: The author determines the time required for the population to triple and quadruple. The rate of increase of population is proportional to the number of people present.

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Determine the time required for the population to triple and the time required for the population to quadruple.

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Chapter 2 Solutions