Explanation Given information: A saving account with $ 500 initial deposit earns 4 % annual interest rate which is compounded continuously. Daily deposits of $ 3 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 = 4 % = 0.04 . In this case growth of P t comes from interest only and which satisfies the equation, y ' = 0.04 × y Taking the deposits into consideration which are added into the account at the rate of $ 3 per day i.e., $ 1095 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 ' = 0.04 y + 1095 Since the initial deposit in the account was $ 500 , it follows that P t satisfies the initial condition y 0 = 500

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Chapter 5.4, Problem 9E

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To find: Pt in Exercise 1 .

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P t in Exercise 1 .

Solution Summary: The author calculates that the rate of change of P(t) is the net effect of these two influences and satisfies the differential equation.

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