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)=800e^-.215t where t is the tim

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)=800e^-.215t where t is the tim      Log On


   



Question 1156715: 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)=800e^-.215t
where t is the time in​ years? Round your answer to the nearest hundredth year

Found 2 solutions by Boreal, josgarithmetic:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
A+Aoe^(-215t)
but A= (1/2)A0
so 1/2=e^(-.215t)
ln of both sides to get rid of e
-ln 2 (because it is ln1-ln2, and ln1 is 0)=-.215t
negative signs go away
t=3.22 years

Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
-----------------
​A(t)=800e^-.215t
----------------



A%28t%29=800e%5E%28-0.215t%29

1%2F2=e%5E%28-0.215t%29
ln%281%2F2%29=-0.215t
etc., etc.