JEE Physics Practice Question

${ }^{131} \mathrm{I}$ is an isotope of Iodine that $\beta$ decays to an isotope of Xenon with a half-life of 8 days. A small amount of a serum labelled with ${ }^{131} \mathrm{I}$ is injected into the blood of a person. The activity of the amount of ${ }^{131} \mathrm{I}$ injected was $2.4 \times 10^{5}$ Becquerel (Bq). It is known that the injected serum will get distributed uniformly in the blood stream in less than half an hour. After 11.5 hours, $2.5 \mathrm{ml}$ of blood is drawn from the person's body, and gives an activity of $115 \mathrm{~Bq}$. What is the total volume of blood in the person's body, in liters is approximately? (you may use $e^{x} \approx 1+x$ for $|x| \ll 1$ and $\ln 2 \approx 0.7$ ).