Question

Ann is competing in a national table-tennis tournament with 128 participants. Each round, half of the participants are eliminated. You can use a function to describe the number of participants remaining in the tournament after x rounds.
Write an equation for the function. If it is linear, write it in the form h(x)=mx+b. If it is exponential, write it in the form h(x)=a(b)x.

Answer 1

Each round halves the field, so the number remaining is exponential:
h(x) = 128(1/2)^x, for x = 0,1,2,...,7.

(Equivalently h(x) = 2^(7−x).)