2nd Edition

ISBN: 9781323178522

Author: Briggs

Publisher: PEARSON

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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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Textbook Question

Chapter D1.4, Problem 42E

Endowment model An endowment is an investment account in which the balance ideally remains constant and withdrawals are made on the interest earned by the account. Such an account may be modeled by the initial value problem B′(t) = rB – m, for t ≥ 0, with B(0) = B₀. The constant r > 0 reflects the annual interest rate, m > 0 is the annual rate of withdrawal, B₀ is the initial balance in the account, and t is measured in years.

a. Solve the initial value problem with r = 0.05, m = $1000/year, and B₀ = $15,000. Does the balance in the account increase or decrease?

b. If r = 0.05 and B₀ = $50,000, what is the annual withdrawal rate m that ensures a constant balance in the account? What is the constant balance?

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Chapter D1.4, Problem 41E

Chapter D1.4, Problem 43E

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Chapter D1 Solutions

CODE/CALC ET 3-HOLE

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Solution Summary: The author explains the initial value for the given differential equation and to check whether the balance decreases or increases.

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