SOLUTION: Use the exponential decay equation, where A is the amount of a radioactive material present after time t, k is the half-life of the radioactive material, and A(base 0) is the origi

Algebra ->  Equations -> SOLUTION: Use the exponential decay equation, where A is the amount of a radioactive material present after time t, k is the half-life of the radioactive material, and A(base 0) is the origi      Log On


   

Question 1060125: Use the exponential decay equation, where A is the amount of a radioactive material present after time t, k is the half-life of the radioactive material, and A(base 0) is the original amount of radioactive substance.

A 5 microgram sample of a radioactive isotope decays to 4.23 micrograms in 9 min. What is the half-life of the radioactive isotope, in minutes? (Round your answer to two decimal places.)
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Use the exponential decay equation, where A is the amount of a radioactive material present after time t, k is the half-life of the radioactive material, and A(base 0) is the original amount of radioactive substance.
A = Ao*2^(-t/k)
:
A 5 microgram sample of a radioactive isotope decays to 4.23 micrograms in 9 min.
What is the half-life of the radioactive isotope, in minutes?
A = 5 micrograms
Ao = 4.23
t = 9 min
:
5 * 2(-9/k) = 4.23
2(-9/k) = 4.23%2F5
using nat logs
-9%2Fkln(2) = ln%284.23%2F5%29
-9%2Fk * .693 = -.167
-9%2Fk = -.167%2F.693
-9%2Fk = -.241
k = %28-9%29%2F%28-.241%29
k = +37.34 days
:
;
Check this on your calc: enter 5 * 2^(-9/37.34) =





(Round your answer to two decimal places.