Answer:
16.19 days.
Step-by-step explanation:
The radioactive iodine is used to determine the health of the thyroid gland and it decays according to the equation [tex]y = a(e)^{- 0.0856t}[/tex] where t is in days and a is the initial amount and y is the final amount after decay for t days.
We have to find a one-fourth life of this substance.
So, [tex]\frac{a}{4} = a(e)^{- 0.0856t}[/tex]
⇒ [tex]\frac{1}{4} = 0.25 = e^{- 0.0856t}[/tex]
Now, taking ln both sides we get,
ln (0.25) = - 0.0856t ln e {Since, [tex]\ln a^{b} = b \ln a[/tex]}
So, t = 16.19 days. (Answer)
