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If 250 mg of a radioactive element decays to 200 mg in 12 hours, find the half-life of the element. (Round your answer to the nearest whole number.)

Guest Apr 19, 2018

#1**+1 **

200 = 250 x 1/2^(12/t), where t=half-life

0.8 = 1/2^(12/t) Take the natural log of both sides

-0.22314355 =(12/t) x -0.69314718 Cross multiply

-0.22314355 t =-8.317766 Divide both sides by -0.22314355

t = 37.275 =~**37 hours - the half-life of this material.**

Guest Apr 19, 2018

#2**+1 **

We have that

200 = 250(.5)^(12/h) where h is the half-life in hours

Divide both sides by 250

200/250 = (.5)^(12/h)

.8 = (.5)^(t/h) take the log of both sides

log (.8) = log(.5)^(12/h)

And by a log property we can write

log (.8) = (12/h) log (.5)

Rearrange to isolate h

h = 12log(.5) / log(.8) ≈ 37.28 hrs

CPhill Apr 19, 2018