Answer:
It will take 60 days for half of the Iodine-125 to decay
Step-by-step explanation:
The amount of iodine-125 after t days is given by the following equation:
[tex]Q(t) = Q(0)(1-r)^{t}[/tex]
In which Q(0) is the initial amount and r is decay rate, as a decimal.
Decay rate of 1.15% per day.
This means that [tex]r = 0.0115[/tex]
So
[tex]Q(t) = Q(0)(1-r)^{t}[/tex]
[tex]Q(t) = Q(0)(1-0.0115)^{t}[/tex]
[tex]Q(t) = Q(0)(0.9885)^{t}[/tex]
To the nearest day, how long will it take for half of the Iodine-125 to decay?
This is t for which [tex]Q(t) = 0.5Q(0)[/tex]
So
[tex]Q(t) = Q(0)(0.9885)^{t}[/tex]
[tex]0.5Q(0) = Q(0)(0.9885)^{t}[/tex]
[tex](0.9885)^{t} = 0.5[/tex]
[tex]\log{(0.9885)^{t}} = \log{0.5}[/tex]
[tex]t\log{0.9885} = \log{0.5}[/tex]
[tex]t = \frac{\log{0.5}}{\log{0.9885}}[/tex]
[tex]t = 59.93[/tex]
To the nearest day
It will take 60 days for half of the Iodine-125 to decay
