SOLUTION: Hello, I am building a study guide and I need a working example of this problem so I can study it for the exam next week. Can someone help me solve, thank you. The decay rate o

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Question 1130962: Hello, I am building a study guide and I need a working example of this problem so I can study it for the exam next week. Can someone help me solve, thank you.
The decay rate of a certain chemical is 9.5​% per year. What is its ​half-life? Use the exponential decay model ​P(t)
=P0e subscript -kt where k is the decay​ rate, and P0 is the original amount of chemical.
The​ half-life of the chemical is ______years.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
P%28t%29=P%5Bo%5De%5E%28-kt%29

Your 9.5% per year information will allow you to find k.
1-0.095=1%2Ae%5E%28-k%2A1%29
0.905=e%5E%28-k%29
From this, take natural log of both sides and find k.

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Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Hello, I am building a study guide and I need a working example of this problem so I can study it for the exam next week. Can someone help me solve, thank you.
The decay rate of a certain chemical is 9.5​% per year. What is its ​half-life? Use the exponential decay model ​P(t)
=P0e subscript -kt where k is the decay​ rate, and P0 is the original amount of chemical.
The​ half-life of the chemical is ______years.
matrix%281%2C3%2C+P%28t%29%2C+%22=%22%2C+P%5Bo%5De%5E%28-+kt%29%29

matrix%281%2C3%2C+1%2F2%2C+%22=%22%2C+e%5E%28-+.095t%29%29 ------- Substituting 1%2F2 for P(t), and .095 (9.5%) for k

matrix%281%2C3%2C+-+.095t%2C+%22=%22%2C+ln+%281%2F2%29%29

Half-life of the chemical, or