1.21 The Explanation (Section 1.2.2) discussed two financial situations: one in which Shannon earns money at a consistent (linear) rate, and one in which she continuously earns interest on her money. Now suppose both are going on at the same time. Shannon makes $30,000/year salary, and her money always goes immediately into the bank, where it earns interest at an annual rate of 10%. (a) Write the differential equation that says Shannons money increases every year by $30,000 plus 10% of whatever she has. Use M for the total of her money and t for time in years. (To make the answer look nicer, measure M in thousands of dollars instead of dollars.) (b) Assuming Shannon starts with no money, show that the function M(t) = 300(et10 1) satisfies both the differential equation and the initial condition. (c) We were able to write our solution in that form because we had already specified what units we were using for time and money. To write this solution with correct units, so that it would be valid for any units of time and money, we can write M(t) = D(etk 1), where D = 300 and k = 10. What are the units of D and k?