Answer: [tex]7.949\ \text{days}[/tex]
Step-by-step explanation:
Given
The half-life of a sample is [tex]T_{\frac{1}{2}}=3.823\ \text{days}[/tex]
Decay is given by
[tex]A=A_o2^{\dfrac{-t}{T_{\frac{1}{2}}}}[/tex]
After 3 half-lives, one-eight of the sample is left
Insert the values
[tex]\Rightarrow \dfrac{A_o}{8}=A_oe^{\dfrac{-t}{T_{\frac{1}{2}}}}\\\\\Rightarrow e^{\dfrac{t}{T_{\frac{1}{2}}}}=8\\\\\text{Taking log both sides}\\\Rightarrow \dfrac{t}{T_{\frac{1}{2}}}=\ln 8\\\\\Rightarrow t=3.823\times \ln 8\\\\\Rightarrow t=7.944\ \text{days}[/tex]
