How much Iodine-125 would remain in the tumor after 60 days?

Question

A tumor is injected with 0.6g of Iodine-125, which has a decay rate of 1.15% per day. Write an exponential model representing the amount of Iodine-125 remaining in the tumor after t days. Then use the formula to the amount of Iodine-125 that would remain in the tumor after 60 days.

Answer 1

A(t) = 0.6(1 - 0.0115)^t

a(60) = 0.6(0.9885)⁶⁰

Answer 2

A(t) = 0.6e^-0.0115t where t= number of days

A(60) = 0.6e^-0.0115(60) = 0.6e^-0.69 = 0.6(.5)= 0.3 g

1/2 = e^-.0115t

.5 = e^-.0115t

ln(.5) = -.0115t

t = ln(.5)/-.0115= about 60.27 days

t = = half life=about 60 days

in 60 days the amount left is slightly less than half of .6g = .3 grams