A queen gives a dragon-slaying hero a choice between two prizes. The first provides $100,000 a day for d-days; the second provides an amount of money that doubles in size each day for d-days starting from a penny (so one penny the first day, two pennies the second, four pennies the next, etc.).
a. Provide the formula for the amount of money after d-days provided by each prize.
b. Graph your results for values of d ranging from 0 to 31 days.
c. Using your graph, advice the hero on which prize he should choose depending on the number of days d involved in the queen's offer.