Suppose that the half-life of steroids taken by an athlete is 42 days. Assuming that the steroids biodegrade by a first-order process, how long would it take for of the initial dose to remain in the athlete’s body?

2.4 × 10² days

Explanation:

There is some info missing. I think this is the original question.

Suppose that the half-life of steroids taken by an athlete is 42 days. Assuming that the steroids biodegrade by a first-order process, how long would it take for 1/64 of the initial dose to remain in the athlete’s body?

First, we will calculate the rate constant (k) for this process.

k = ln 2/ (t1/2) = ln 2 / 42 d = 0.017 d⁻¹

We can find the time t so that the concentration of the steroids [A] = 1/64 [A]₀ using the following expression.