SOLUTION: An unknown radioactive element decays into non-radioactive substances. In 820 days the radioactivity of a sample decreases by 28 percent. (a) What is the half-life of the elemen

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: An unknown radioactive element decays into non-radioactive substances. In 820 days the radioactivity of a sample decreases by 28 percent. (a) What is the half-life of the elemen      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1088855: An unknown radioactive element decays into non-radioactive substances. In 820 days the radioactivity of a sample decreases by 28 percent.
(a) What is the half-life of the element?
half-life
(b) How long will it take for a sample of 100 mg to decay to 63 mg?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
So if you started with 100g, in 820 days you'd have %280.72%29%28100g%29=72+g.
So then,
72=100e%5E%28k%28820%29%29
e%5E%28820k%29=0.72
820k=ln%280.72%29
k=ln%280.72%29%2F820
k=-4.006x10%5E%28-3%29
.
.
.
a) 50=100e%5E%28kt%29
e%5E%28kt%29=1%2F2
kt=ln%281%2F2%29
t%5B1%2F2%5D=ln%281%2F2%29%2Fk
t%5B1%2F2%5D=ln%281%2F2%29%2A%28820%2Fln%280.72%29%29
t%5B1%2F2%5D=1730days
.
.
.
b)63=100e%5E%28kt%29
t=+ln%280.63%29%2A%28820%2Fln%280.72%29%29+
t=1153days