# Engineering Math

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.

1. Damon

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

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