SOLUTION: If anyone can help me solve this, I would be so appreciative. This is day two of trying to solve this successfully. Thanks. The amount of​ carbon-14 present in animal bo

Algebra ->  Probability-and-statistics -> SOLUTION: If anyone can help me solve this, I would be so appreciative. This is day two of trying to solve this successfully. Thanks. The amount of​ carbon-14 present in animal bo      Log On


   

Question 1130958: If anyone can help me solve this, I would be so appreciative. This is day two of trying to solve this successfully. Thanks.
The amount of​ carbon-14 present in animal bones after t years is given by ​P(t)
=P0e superscript−0.00012t. A bone has lost 11​% of its​ carbon-14. How old is the​ bone?
The bone is ____________years old.
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
p=p%5Bo%5De%5E%28-0.00012t%29

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p=1-0.11
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p%5Bo%5D=1
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Take natural logs of both sides and solve for t.

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The bone has lost 11% of its Carbon-14, so the percent remaining is 89%; the fraction remaining is 0.89. The fraction remaining is the current amount, P(t), divided by the original amount, P(0). So

P%28t%29%2FP%280%29+=+0.89

The given formula for the amount remaining is

P%28t%29+=+P%280%29%2Ae%5E%28-0.00012t%29

That formula is equivalent to

P%28t%29%2FP%280%29+=+e%5E%28-0.00012t%29

So we want to solve for the number of years t in the equation

e%5E%28-0.00012t%29+=+0.89

Since the exponential is base e, take the natural log of both sides of the equation:

-0.00012t+=+ln%280.89%29

t+=+ln%280.89%29%2F-0.00012%29 = 971 years to the nearest whole number