Beth initially deposits $400 in a savings account that pays interest at the rate of 3% per year compounded continuously. She also arranges for $10 per week to be de-posited automatically into the account.
(a) Assume that weekly deposits are close enough to continuous deposits so that we can reasonably approximate her balance using a differential equation. Write an initial-value problem for her balance over time.
(b) Approximate Beth's balance after 4 years by solving the initial-value problem in part (a).
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