Question

Shauna dropped 260 quarters on the ground. She removed all the quarters that landed on heads and then counted all the quarters that landed on tails. She then picked up all the quarters that landed on tails and dropped them again. She continued the pattern of removing the heads, counting the tails, and then re-dropping all the quarters that landed on tails. Write an equation that can be used to model the number of quarters landing on tails T, after d drops.

Answer 1

The equation to model the number of quarters landing on tails after d drops is T = 260 * (0.5)^d, reflecting exponential decay as the number of quarters is halved with each drop.

Step-by-step explanation:

The student's question involves creating a mathematical model to describe the number of quarters landing on tails (T) after d drops. Since each time Shauna drops the quarters, each has a 50 percent chance of landing on tails, we can represent this scenario using an equation that models exponential decay, as each subsequent drop effectively halves the number of quarters.

The equation that models the number of quarters landing on tails after d drops is:

T = 260 * (0.5)^d

Here, 260 represents the initial number of quarters, 0.5 is the probability of a quarter landing on tails for a single drop, and d is the number of times the remaining quarters are dropped.