SOLUTION: Use Q(t)=Q sub 0 e^kt to solve: Find the half-life of a radioactive substance if 240 grams of the substance decays to 180 grams in 9 years. Please, please, please, help? Thank y

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Question 822995: Use Q(t)=Q sub 0 e^kt to solve: Find the half-life of a radioactive substance if 240 grams of the substance decays to 180 grams in 9 years.
Please, please, please, help? Thank you!
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

Find the half-life of a radioactive substance 

if 240 grams of the substance decays to 180 grams in 9 years.

The Idea is to 'personalize' Q%28t%29=Q%5B0%5De%5E%28-kt%29+ by finding the 'k' value

according to the information given.

180/240 = e^-kt

 .75 = e^-9k

 ln(.75)/-9 =  k  = .0320

 Q%28t%29=Q%5B0%5De%5E%28-.0320t%29+

 Find the half-life of this radioactive substance: Q%28t%29%2FQ%5B0%5D+=+1%2F2

  .5+=+e%5E%28-.0320t%29+

  ln(.5)/-.0320 = t = 21.66 yrs