Number Theory If you tear a piece of paper that is 0.005 centimeter thick in half, and place the two pieces on top of each other, the height of the pile of paper is 0.01 centimeter. Let's call this the second pile. If you tear these two pieces of paper in half, the third pile will have four pieces of paper in it.
a. How high is the third pile? the fourth pile?
b. Write a formula to determine how high the nth pile is.
c. Use the formula to determine in theory how high the 10th pile would be and how high the 100th pile would be.