Question

A 15 g sample of radioactive iodine decays in such a way that the mass remaining aftertdays is given bym(t) = 15e−0.087t, wherem(t) is measured in grams. After how many days are there only 5 g remaining?

Answer 1

After 12.62 days

Step-by-step explanation:

The iodine decays following the formula:

`m(t)=15g*e^(-0.087*t)`

Where:

• m is the remaining mass
• t is the time

So, knowing that the remaining mass is 5 g:

`5g=15g*e^(-0.087*t)`

`(1)/(3)=e^(-0.087*t)`

Applying logarithm to both sides:

`ln((1)/(3))=ln(e^(-0.087*t))`

`ln((1)/(3))=-0.087*t*ln(e)`

`(ln(1/3))/(ln(e))=-0.087*t`

Solving:

`-0.087*t=-1.098`

`t=12.62`