SOLUTION: A scientist begins with 250 grams of a radioactive substance. After 250 minutes, the sample has decayed to 32 grams. Rounding to five significant digits, what is the exponential eq

Algebra ->  Rational-functions -> SOLUTION: A scientist begins with 250 grams of a radioactive substance. After 250 minutes, the sample has decayed to 32 grams. Rounding to five significant digits, what is the exponential eq      Log On


   

Question 1138144: A scientist begins with 250 grams of a radioactive substance. After 250 minutes, the sample has decayed to 32 grams. Rounding to five significant digits, what is the exponential equation representing this situation. To the nearest minute, what is the half life of this substance?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Let n be the number of half-lives in 250 minutes. Then since the original 250g has decayed to 32g in those 250 minutes,

%28.5%29%5En+=+32%2F250+=+0.128
n%2Alog%28%28.5%29%29+=+log%28%280.128%29%29
n+=+log%28%280.128%29%29%2Flog%28%28.5%29%29 = 2.965784 to 6 decimal places.

So the half-life in minutes is

250%2F2.965784 = 84.294735.

If you want the half-life to the nearest minute, it is 84 minutes.

Then, if you want to use that rounded number in the exponential equation, the equation is

y = A(.5)^(t/84)