# Problem: 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?

###### FREE Expert Solution

The integrated rate law for a first-order reaction is as follows:

where:

[A]t = concentration at time t
k = rate constant
t = time
[A]0 = initial concentration

Calculate k:

k = 0.0165 days-1

Solving for time t:

let [A]0 = 1

[A]t = 1/64

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###### Problem Details

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?