SOLUTION: Last one tonight and I believe this will help complete my study guide for this chapter. Thank you in advance. The decay rate of a certain chemical is 9.5​% per year. What

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Question 1130481: Last one tonight and I believe this will help complete my study guide for this chapter. Thank you in advance.
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 Superscript -kt)
−kt where k is the decay​ rate, and P0 is the original amount of chemical.
The​ half-life of the chemical is ___years.
​(Round to the nearest​ integer.)
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
Model is , and half life is value of t when .

FIND k, first.
Some variables changes just for notational and keyboard conveniences.
y=p*e^(-kt) instead of and ;

, one year of decay time





Model can be stated .

FIND HALF-LIFE
Using model as
take natural logs of both sides, simplify, and solve for t.
result should be .
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
Last one tonight and I believe this will help complete my study guide for this chapter. Thank you in advance.
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 Superscript -kt)
−kt where k is the decay​ rate, and P0 is the original amount of chemical.
The​ half-life of the chemical is ___years.
​(Round to the nearest​ integer.)
 



 ------- Substituting 

 ----- Converting to LOGARITHMIC (Natural) form

 

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