Students in an Algebra 1 class will perform the following experiment and then model it mathematically. They begin with 128 two-colored counters (a chip that has a yellow side and a red side) in a bag and complete the following steps:

Pour the counters from the bag onto the floor.
Count the number of counters that land on yellow.
Record the trial number and the number of counters that landed on yellow.
Put the counters that landed on yellow back into the bag and leave the rest on the floor (off to the side).
Steps 1 to 4 constitute one trial of the experiment. Repeat trials until no counters land on yellow.

Question 1
POSSIBLE POINTS: 1
Part A

Select the equation that best represents f(n), the number of yellow counters that land on yellow (and are put back into the bag) at the end of trial n, when n≥1?


A f(n)=128(12)nf of n is equal to 128 times 1 half to the n th power

B f(n)=128−12nf of n is equal to 128 minus 1 half n
Question 2

Part B

How many trials would the students most likely need to run until exactly one counter lands yellow side up (and is put into the bag)? Use mathematics to justify your response.