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#1 If $50,000 is deposited in an account that earns 5% interest compounded continuously, then the amount in the account after t years is given by the function: f(t) = 500000.05 (a) How long will it take for the balance to reach $100000? (b) What is the average rate of change in the account from the 2nd year (t = 2) until the 5th year (t = 5)? Explain the meaning of the number you compute. (e) What is the instantaneous rate of change in the account in the 3rd year (t = 3)? Explain the meaning of the number you compute. (d) Find the time I guaranteed to exist by the Mean Value Theorem for which the instantaneous rate of change equals the average rate of change in the account during the time period from 1 = 2 to = 5. (e) [Extra credit] What annually compounded rate of interest is equivalent to the 5% continuously compounded rate over a 10 year period