SOLUTION: The half-life of a substance is 7 hours, Using A=A0eKT, Find K

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Question 966028: The half-life of a substance is 7 hours, Using A=A0eKT, Find K
Answer by josgarithmetic(39615) About Me  (Show Source):
You can put this solution on YOUR website!
This, A=A0eKT, does not mean what you want it to mean.

THIS means what you want, using pure text: A=A[0]e^(KT)

Inside the rendering tags, you find A=A%5B0%5De%5E%28KT%29.

Now to solve for K, take logarithms of the left and right sides, and then substitute appropriate values:

ln%28A%29=ln%28A%5B0%5D%29-KT%2Aln%28e%29

ln%28A%29-ln%28A%5B0%5D%29=-KT%2A1

KT=ln%28A%5B0%5D%29-ln%28A%29

K=%28ln%28A%5B0%5D%29-ln%28A%29%29%2FT

highlight_green%28K=ln%28A%5B0%5D%2FA%29%2FT%29

Then substitution,
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highlight%28K=ln%282%29%2F7%29