Question: A person planning for her retirement arranges to make continuous deposits into a savings account at the rate of $3600 per year. The savings account

A person planning for her retirement arranges to make continuous deposits into a savings account at the rate of $3600 per year. The savings account earns 5% interest compounded continuously.

(a) Set up a differential equation that is satisfied by f (t), the amount of money in the account at time t.

(b) Solve the differential equation in part (a), assuming that f (0) = 0, and determine how much money will be in the account at the end of 25 years.

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