Savings Account Let A(t) be the balance (in dollars) in a savings account after t years, and
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Question:
Savings Account Let A(t) be the balance (in dollars) in a savings account after t years, and suppose that A(t) satisfies the differential equation
A'(t) = .045 A(t), A(0) = 3000.
(a) How much money was originally deposited in the account?
(b) What interest rate is being earned?
(c) Find the formula for A(t).
(d) What is the balance after 5 years?
(e) Use part (d) and the differential equation to determine how fast the balance is growing after 5 years.
(f ) How large will the balance be when it is growing at the rate of $270 per year?
Show full calculation and provide units when applicable.
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