Question

radioactive iodine is used to determine the health of the thyroid gland it decays according to the equation y=ae^-0.0856t where t is in days find one fourth life of this substance

Answer 1

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 $y = a(e)^{- 0.0856t}$ 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, $\frac{a}{4} = a(e)^{- 0.0856t}$

⇒ $\frac{1}{4} = 0.25 = e^{- 0.0856t}$

Now, taking ln both sides we get,

ln (0.25) = - 0.0856t ln e {Since, $\ln a^{b} = b \ln a$}

So, t = 16.19 days. (Answer)