SOLUTION: A certain radioactive isotope has leaked into a small stream. One hundred days after the leak, 14% of the original amount of the substance remained. Determine the half-life o
Algebra ->
Customizable Word Problem Solvers
-> Evaluation
-> SOLUTION: A certain radioactive isotope has leaked into a small stream. One hundred days after the leak, 14% of the original amount of the substance remained. Determine the half-life o
Log On
Question 1139086: A certain radioactive isotope has leaked into a small stream. One hundred days after the leak, 14% of the original amount of the substance remained. Determine the half-life of this radioactive isotope. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! A certain radioactive isotope has leaked into a small stream.
One hundred days after the leak, 14% of the original amount of the substance remained.
Determine the half-life of this radioactive isotope.
:
The radio-active decay formula: A = Ao*2^(-t/h), where:
A = amt of substance remains after t time
Ao = initial amt
t = time of decay
h = half-life of substance
:
Ao = 1,
A = .14
t = 100 days
1*2^(-100/h) = .14
using natural logs
ln(2^(-100/h) = ln(.14)
log equiv of exponents *ln(2) = ln(.14)
: =
find the antilog = -2.8365
h =
h = 35.25 days is the half life of the substance
