SOLUTION: A radioactive substance decays according to A=A0e−0.0048t, where A0 is the initial amount and t is the time in years. If A0=580 grams, find the time for the radioactive substanc

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: A radioactive substance decays according to A=A0e−0.0048t, where A0 is the initial amount and t is the time in years. If A0=580 grams, find the time for the radioactive substanc      Log On


   

Question 1140195: A radioactive substance decays according to A=A0e−0.0048t, where A0 is the initial amount and t is the time in years. If A0=580 grams, find the time for the radioactive substance to decay to 405 grams. Round your answer to two decimal places, if necessary.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
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A=A0e−0.0048t A=A%5Bo%5De%5E%28-0.0048t%29, where A0 is the initial amount and t is the time in years. If A0=580 grams, find the time for the radioactive substance to decay to 405 grams.
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ln%28A%29=ln%28A%5Bo%5D%29%2Bln%28e%5E%28-0.0048t%29%29
ln%28A%29=ln%28A%5Bo%5D%29-0.0048t
ln%28A%29-ln%28A%5Bo%5D%29=-0.0048t
ln%28A%5Bo%5D%29-ln%28A%29=0.0048t
t=%28ln%28A%29-ln%28A%5Bo%5D%29%29%2F0.0048
This is as a formula. You substitute the given values and evaluate.