SOLUTION: given that the half life of a certain radioactive substance s 20 days and there are 5 grams present initially, the equation that models the situation is s(t)=5(1/2)^t/20. Find the

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: given that the half life of a certain radioactive substance s 20 days and there are 5 grams present initially, the equation that models the situation is s(t)=5(1/2)^t/20. Find the       Log On


   

Question 546806: given that the half life of a certain radioactive substance s 20 days and there are 5 grams present initially, the equation that models the situation is s(t)=5(1/2)^t/20. Find the time when here will be 1 gram of the substance remaining
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
So you have the equation s%28t%29=5%281%2F2%29%5E%28t%2F20%29,
and want to find the time, t, until you have s%28t%29=1%7D%7D+gram+left.%0D%0AThe+equation+is+%7B%7B%7B5%281%2F2%29%5E%28t%2F20%29=1.
That is a job for logarithms. Logarithm (base 10 is OK) of the left side is equal to logarithm of 1, which is zero. Let's work on the left side:

So, log%285%29-t%2Alog%282%29%2F20=0 ---> t%2Alog%282%29%2F20=log%285%29 ---> t=20%2Alog%285%29%2Flog%282%29
The approximate answer (according to my calculator) is t=46.44 days (46 days and 10.5 hours)