Answer:
After 12.62 days
Explanation:
The iodine decays following the formula:
[tex]m(t)=15g*e^{-0.087*t}[/tex]
Where:
- m is the remaining mass
- t is the time
So, knowing that the remaining mass is 5 g:
[tex]5g=15g*e^{-0.087*t}[/tex]
[tex]\frac{1}{3}=e^{-0.087*t}[/tex]
Applying logarithm to both sides:
[tex]ln(\frac{1}{3})=ln(e^{-0.087*t})[/tex]
[tex]ln(\frac{1}{3})=-0.087*t*ln(e)[/tex]
[tex]\frac{ln(1/3)}{ln(e)}=-0.087*t[/tex]
Solving:
[tex]-0.087*t=-1.098[/tex]
[tex]t=12.62[/tex]
