SOLUTION: how long will it take a sample of radioactive substance to decay to half of its original amount, if it decays according to the function A(t)=700e-0.033t, where t is the time in yea

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: how long will it take a sample of radioactive substance to decay to half of its original amount, if it decays according to the function A(t)=700e-0.033t, where t is the time in yea      Log On


   

Question 932814: how long will it take a sample of radioactive substance to decay to half of its original amount, if it decays according to the function A(t)=700e-0.033t, where t is the time in years? round to the nearest hundredth year.

please show all the steps.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
The model must be written, highlight_green%28A%28t%29=700%2Ae%5E%28-0.033t%29%29. You want to solve for t in 1%2F2=1%2Ae%5E%28-0.033t%29. Take natural log of both sides.

ln%281%2F2%29=-0.033t%2A1
t=ln%281%2F2%29%2F%28-0.033%29
highlight%28t=ln%282%29%2F0.033%29
21 years