🤓 Based on our data, we think this question is relevant for Professor Bairu's class at CSUEASTBAY.

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

$\overline{){\mathbf{ln}}{\mathbf{}}{\mathbf{\left[}\mathbf{A}\mathbf{\right]}}_{{\mathbf{t}}}{\mathbf{=}}{\mathbf{-}}{\mathbf{kt}}{\mathbf{+}}{\mathbf{ln}}{\mathbf{}}{{\mathbf{\left[}}{\mathbf{A}}{\mathbf{\right]}}}_{{\mathbf{0}}}}$

where:

**[A] _{t}** = concentration at time t

**Calculate k:**

$\overline{){{\mathbf{t}}}_{\raisebox{1ex}{$\mathbf{1}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{2}$}\right.}{\mathbf{=}}\frac{\mathbf{ln}\mathbf{}\mathbf{2}}{\mathbf{k}}}\phantom{\rule{0ex}{0ex}}\mathbf{k}\mathbf{=}\frac{\mathbf{ln}\mathbf{}\mathbf{2}}{{\mathbf{t}}_{{\displaystyle \raisebox{1ex}{$\mathbf{1}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{2}$}\right.}}}\phantom{\rule{0ex}{0ex}}\mathbf{k}\mathbf{=}\frac{\mathbf{ln}\mathbf{}\mathbf{2}}{\mathbf{42}\mathbf{}\mathbf{days}}$

**k = 0.0165 days ^{-1}**

**Solving for ****time t****:**

let [A]_{0} = 1

[A]_{t} = 1/64

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?

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What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Integrated Rate Law concept. You can view video lessons to learn Integrated Rate Law. Or if you need more Integrated Rate Law practice, you can also practice Integrated Rate Law practice problems.

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Based on our data, we think this problem is relevant for Professor Bairu's class at CSUEASTBAY.

What textbook is this problem found in?

Our data indicates that this problem or a close variation was asked in Chemistry - OpenStax 2015th Edition. You can also practice Chemistry - OpenStax 2015th Edition practice problems.