SOLUTION: A box contains a radioactive substance. The number of kilograms r(t) at time t years is given by the formula r(t) = 2^-0.002149t. How long will it take until only one-half kilogram

Algebra ->  Test  -> Lessons -> SOLUTION: A box contains a radioactive substance. The number of kilograms r(t) at time t years is given by the formula r(t) = 2^-0.002149t. How long will it take until only one-half kilogram      Log On


   

Question 319086: A box contains a radioactive substance. The number of kilograms r(t) at time t years is given by the formula r(t) = 2^-0.002149t. How long will it take until only one-half kilogram of the radioactive substance is left in the box?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
r%28t%29+=+2%5E%28-0.002149t%29
Find t so that,
2%5E%28-0.002149t%29=0.5
-0.002149t=log%282%2C%28%280.5%29%29%29
t=log%282%2C%28%280.5%29%29%29%2F%28-0.002149%29
t=%28log%28%280.5%29%29%2Flog%28%282%29%29%29%2A%281%2F%28-0.002149%29%29
t=%28%28-0.301%29%2F%280.301%29%29%2A%281%2F%28-0.002149%29%29
t=465 years