SOLUTION: A radioactive substance has a half-life of 200 years. We currently have 15 grams of the substance.
How long until only .5 grams of the substance remains radioactive?
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Question 194462: A radioactive substance has a half-life of 200 years. We currently have 15 grams of the substance.
How long until only .5 grams of the substance remains radioactive?
Could you please provide a detailed explanation of how you achieved the solution. Thanks!
Answer by Edwin McCravy(20060) (Show Source): You can put this solution on YOUR website!
A radioactive substance has a half-life of 200 years. We currently have 15 grams of the substance.
How long until only .5 grams of the substance remains radioactive?
Could you please provide a detailed explanation of how you achieved the solution. Thanks!
The exponential growth and decay formula is
Where A = the final amount
P = the beginning amount
r = the rate (positive for growth, negative
for decay. This is a decay problem so
we expect r to be negative)
t = the time that has lapsed
e = 2.718...
When t = 0, A = 15
Substitute 15 for P in
Since the substance has a half-life of 200
years, then there will only be half of 15
grams present, so
when t = 200, A = 7.5, half of 15 grams.
So we substitute that and get
Use the fact that the equation
is equivalent to
Will finish later.
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