Explanation Given information: An investment account grows at an annual rate of 10 % compounded continuously. The account was open with an initial deposit of $1500 and monthly deposits of $ 800 are made into the account. Formula used: The solution of initial value problem y ' = r y + k , y 0 = p 0 is y = p 0 + k r e r t − k r . Calculation: If no deposits or withdrawals are made, then only interest is being added to the account at a rate proportional to the amount in the account with constant of proportionality r = 10 % = 0.1 . In this case growth of P t comes from interest only and which satisfies the equation, y ' = 0.1 × y Taking the deposits into consideration which are added into the account at the rate of $ 800 per month i.e., $ 9600 per year then the amount of money in the account changes in two ways − the rate at which interest is added and the rate at which deposits are made. The rate of change of P t is the net effect of these two influences and it satisfies the differential equation- y ' = 0.1 y + 9600 Since the initial deposit in the account was $ 1500 , it follows that P t satisfies the initial condition y 0 = 1500

12th Edition

ISBN: 9780137590810

Author: Larry J. Goldstein, David C. Lay, David I. Schneider, Nakhle H. Asmar, William Edward Tavernetti

Publisher: PEARSON

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Chapter 5.4, Problem 10E

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To find: Pt in Exercise 4 .

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Calculus & Its Applications

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P t in Exercise 4 .

Solution Summary: The author explains that an investment account grows at an annual rate of 10% compounded continuously.

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