Question

# Use your equation to determine the half-life ofthis type of Fodine, That is, find out how many days it will take for half of the original amount to be left. Show an algebraic solution using logs

Modeling
Use your equation to determine the half-life ofthis type of Fodine, That is, find out how many days it will take for half of the original amount to be left. Show an algebraic solution using logs

2020-12-01
To find the half life of iodine (i.e) $$t =\ ?\ when\ P=\frac{P_{0}}{2}=\ \frac{10}{2}=5$$ grams of iodine $$P = 10_{e}^{−0.086t}$$ substitute $$P = 5$$ in the above equation $$5 = 10_{e}^{−0.086t}$$ Dividing both sides by 10 we get, $$\frac{5}{10}=e^{-0.086t}$$
$$\Rightarrow\ e^{-0.086t}=\ \frac{1}{2}$$
$$e^{0.086t} = 2$$ Taking log on both sides we get, $$0.086t = \log_{e} 2$$
$$\Rightarrow\ t=\ \frac{\log_{e}2}{0.086}=\ \frac{0.69310}{0.086}=8.0598\ \approx\ 8$$ Therefore it took 8 days for the iodine reduces to 5 grams