Congratulations, you are the million dollar jackpot winner! Now you have to make the following decision: Either you take 25 annual payments of $50,000 each, or a lump sum of $1,000,000 up front. Use your knowledge of first-order differential equations to help you arrive at a decision. (Of course, 25 times $50,000 is $1, 250,000, but getting the million up front allows you to invest it immediately.) (a) First ignore inflation, and assume that you will invest money at a growth rate r, which you may assume is constant over 25-year time period of payout. How does your choice depend on the value of r? (b) In the scenario of part (a), what is the threshold rate r? That is, the value of r for which the two different payout plans yield exactly the same amount of money after 25 years. (c) Now include an inflation rate rho, with rho