Your state lottery is offering a choice of pay out options with the next Powerball drawing. Winners of the Powerball can choose between 1 billion dollars or they may choose to start with $2 on day one, double it the next day to $4, double it again the third day to $8, and so on for a term of 30 days. a) Create a chart to help you find a pattern in the second payout option then write a formula.

b) Which payout option would you choose? Show all your calculations and explain which choice you would make.

c) How much money would you have if the term was 45 days? Express your answer in both standard and scientific notation.