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

16.19 days.

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,
`(a)/(4) = a(e)^(- 0.0856t)`

⇒
`(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)