Answer:
The decay rate of the medication is approximately [tex]0.116\,\frac{1}{h}[/tex].
Step-by-step explanation:
If we know that amount of medication decays exponentially, this amount is represented by the following expression:
[tex]n(t) = n_{o}\cdot e^{-\lambda\cdot t}[/tex] (1)
Where:
[tex]n_{o}[/tex] - Initial amount of medication.
[tex]n(t)[/tex] - Current amount of medication.
[tex]t[/tex] - Time, measured in hours.
[tex]\lambda[/tex] - Decay rate, measured in [tex]\frac{1}{h}[/tex].
In addition, the decay rate is determined by the following formula:
[tex]\lambda = \frac{\ln 2}{t_{1/2}}[/tex] (2)
If we know that [tex]t_{1/2} = 6\,h[/tex], then the decay rate is:
[tex]\lambda = \frac{\ln 2}{6\,h}[/tex]
[tex]\lambda \approx 0.116\,\frac{1}{h}[/tex]
The decay rate of the medication is approximately [tex]0.116\,\frac{1}{h}[/tex].
