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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)

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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