Radioactive decay of the isotope $^{131}I $ follows first order kinetics. Its half-life time amounts to 8 days. Calculate what fraction remains in a patient 20 days after the date of the absorption of this isotope.
Half-life time: $\theta=8\cdot 3600 \;s$ Rate constant: $k$ $=$ $\frac{ln2}{\theta}$ $=$ $\frac{0.693}{28800}$ $=$ $2.4\cdot 10^{-5}$ Remaining fraction after $t=20 \cdot 3600 \;s$: $\frac{[A]_t}{[A]_o}$ $=$ $e^{-2.4\cdot 10^{-5}\cdot 7.2\cdot 10^4}$ $=$ $e^{-1.73}$ $=$ $0.178$
