. Sweepstakes II: Youve won a national sweepstakes that will give you an income of $100

Chapter 7, Problem 2

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. Sweepstakes II: Youve won a national sweepstakes that will give you an income of $100 a day for the rest of your life! You put the money into a savings account at a bank (Figure 7-3h), where it earns interest at a rate directly proportional to the amount, M, in the account. Assume that the $100 per day rate is continuous, so that dM/dt equals 100 + kM, where k is a proportionality constant. Solve this differential equation subject to the initial condition that you had no money in the account at t = 0 days. Find the proportionality constant if the interest rate is 0.02% (not 2% !) per day, or roughly 7% per year. Transform the solution so that M is in terms of t. Use your result to explore how M varies with t. (A graph might help.) Consider such information as how much of M and of dM/dt comes from the $100 per day and how much comes from interestafter various numbers of days. What is thelimit of M as t approaches infinity?Figure 7-3h