posted by Erica .
An unknown radioactive element decays into non-radioactive substances. In 120 days the radioactivity of a sample decreases by 59 percent.
What is the half life of the element?
How long will it take for a sample of 100 mg to decay to 77 mg?
The answer is not 93 day, I calculated it using the half life formula, but the program says that is not the answer.
My instructor said to set up two equations.
Heres what I have, so far.
A(t=120) = 0.41*A0, and
A(t_1/2) = 0.5*A0.
I didn't know what A0 was... and where to go from there.
Engineering Math -
x = Xi e^-kt
.41 = e^-120k
ln.41 = -120 k
k = .00743
.5 = e^-.00743 t
ln.5 = -.00743 t
t= 93.3 daya
so I pretty much agree with you
.77 = e^-.00743 t
t = 35.2 days