Final answer:
The half-life of steroids taken by an athlete is 42 days, and the time for a certain fraction of the steroid to remain in the athlete's body can be calculated using the first-order decay process formula.
Step-by-step explanation:
The half-life of the steroids taken by an athlete is 42 days. To determine how long it would take for a certain percentage of the initial dose to remain in the athlete's body, we apply the principles of a first-order decay process. The formula to calculate the time it takes for a certain fraction of a substance to remain is t = (ln(fraction remaining) / ln(2)) × half-life. For example, if we wanted to know when 25% (1/4) of the initial dose remains, we would calculate it as follows: t = (ln(1/4) / ln(2)) × 42 days, which simplifies to t = 2 half-lives × 42 days, therefore t = 84 days. This same method can be used to calculate the time for any given fraction of the steroid to remain.