Algebra/Arithmetic/Exponent Answers

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Problem 1[edit]

You tear a piece of paper in half 5 times. How many scraps of paper are you left with?

Answer

You should have 32, or 2^5, scraps of paper left over. The general solution is:

 P = 2^r, where P is the number of paper scraps and r is the number of times the paper has been torn.

An interesting anecdote related to this problem: it was once commonly believed that a piece of paper could only ever be folded 8 times; thus, when unraveled, the paper could contain at most 256 (2^8) sections. However, this was later proven false when Britney Gallivan folded a paper 12 times, and derived a function for the actual number of folds that could occur.

Problem 2[edit]

Problem from previous page

Answer

Problem 3[edit]

Problem from previous page

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Problem 4[edit]

Problem from previous page

Answer