Question

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.

Answer 1

The number of counters is an illustration of a linear function

• The number of counters that land on yellow is: $f(n) = 128 - \frac 12n$
• The students need 254 trials to have one yellow side up

How to determine the equation

The number of counters is given as:

Count = 128

Each counter is two-colored (i.e. 1/2 yellow and 1/2 red)

So, the equation that represents the number of counters that land on yellow is:

$f(n) = 128 - \frac 12n$

The number of trials to have one yellow side up

When one yellow side is up, we have:

f(n) = 1

So, we have:

$1 = 128 - \frac 12*n$

Subtract 128 from both sides

$-127 = - \frac 12*n$

Multiply both sides by -2

$n =254$

Hence, the student needs 254 trials to have one yellow side up

Read more about linear equations at:

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