A state operates a weekly lottery where the jackpot starts at 100,000 and grows each week until a winning ticket is purchased. The state reclaims some of the lottery winnings by way of a tax on those winnings. If w is the size of the winning jackpot (in dollars), then the corresponding tax is T(w)=.02w^1.2 dollars.
1. Suppose that one week the jackpot is 2,000,000. If a winning ticket is sold, then what are the net winnings, to the nearest dollar?
2. Given a jackpot of 2,000,000, calculate the marginal after-tax winnings. Label Appropriately.
3. Is there a jackpot size where the marginal after-tax winnings changes from positive to negative? If so, find that jackpot size (to the nearest dollar) and explain what is significant (in terms of winnings) about that jackpot size. If no such jackpot size exists, then explai why.