Question

Radioactive iodine is used to determine the health of the thyroid gland. The radioactive iodine decays according to the equation y = n ( e − 0.0856 t ) , where t is in days. Find the half-life of this substance. Round to the nearest day.

Answer 1

Answer:

The half-life of this substance would be 8 day

Step-by-step explanation:

Given equation that shows the amount of the substance after t days,

$y = ne^{-0.0856t}$

Where,

n = initial quantity of the substance

If y = n/2,

$\frac{n}{2}=ne^{-0.0856t}$

$\frac{1}{2}=e^{-0.0856t}$

Taking ln both sides,

$\ln (\frac{1}{2}) = -0.0856t$

$-0.69315 = -0.0856t$

$\implies t =\frac{-0.69315}{-0.0856}=8.0975\approx 8$

Hence, the half-life of this substance would be 8 days.