SOLUTION: Use the exponential decay function P(t) = Poe^kt
Chemistry. The decay rate of krypton-85 is 6.3% per day. What is the half-life?
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Question 173403This question is from textbook introduction to college mathematics
: Use the exponential decay function P(t) = Poe^kt
Chemistry. The decay rate of krypton-85 is 6.3% per day. What is the half-life?
This question is from textbook introduction to college mathematics
Answer by gonzo(654) (Show Source): You can put this solution on YOUR website!
the formula is:
that minus k is important since the exponent has to be negative in a decay problem.
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you are given:
decay rate is 6.3% per day.
this translates to .063 per day which is equal to k since k, in this case, is the decay rate per day.
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you are also asked for the half life.
this means at what point in time will the amount of krypton be half of what it is today.
if = 1 = the amount of krypton today, then = .5 is the amount of krypton when one half life has occurred.
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your equation:
becomes:
which becomes:
which you can solve using the log or ln function of your calculator.
we'll use the log function.
either one will get the same answer.
-----
your equation becomes:
since your equation becomes:
if you divide both sides of this equation by , you get:
which you can solve using your calculator to get:
t = 11.0023362 days
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to prove this is true, plug that value in your original equation for t.
that equation:
becomes:
which becomes:
which becomes:
.5 = .5
-----
value is good.
answer is:
t = 11.0023362
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