Over the course of the twentieth century, advances in medicine and nutrition have significantly increased human life expectancy. This has prompted a debate on whether there is a limit for the human life span, and what that limit might be. (The highest verified age for a human so far was Jeanne Calment of France, who lived to an age of 122 years). Two scientists - Jay Olshansky of the University of Illinois-Chicago and Steven Austad of the University of Alabama - have differing views on the subject. In the year 2000, Austad asserted that by the year 2150 there would be a 150-year old human being. His friend Olshansky disagreed, claiming that the upper limit is would be at most 130 years. In the year 2000, the two scientists made a wager - each placed $150 into an investment account and signed a contract stating that in the year 2150 the heirs of the man who was correct would receive the accumulated amount in the account. a) Suppose that the account averages a 7% annual return over this time span. What will be the amount in the account in the year 2150? b) A report published in a financial magazine estimated that with good market returns, the prize could be worth as much as $200 million by the year 2150. What would be the average annual return needed to accumulate this sum? c) A few years after the initial bet, each scientist doubled their initial investments. Assuming that the fund averages an average annual return of 10%, what will be the amount in the fund in the year 2150?