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? Co

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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) About Me  (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
A+=+Pe%5E%28r%2At%29
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
15+=+Pe%5E%28r%2A0%29
15+=+Pe%5E0
15=P%281%29
15=P
Substitute 15 for P in
A+=+15e%5E%28rt%29
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
7.5+=+15e%5E%28r%2A200%29
7.5%2F15+=+e%5E%28r%2A200%29
.5+=+e%5E%28200r%29
Use the fact that the equation Y=e%5EX
is equivalent to X+=ln%28Y%29
200r=ln%28.5%29
r+=+ln%28.5%29%2F200
r+=+-.0034657359
Will finish later.