SOLUTION: A radioactive substance decats by 5% every hour. Intially rhere are 500g of substance. a. How many grams remain after 6 hours? b. What is the half life substance? c. How

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: A radioactive substance decats by 5% every hour. Intially rhere are 500g of substance. a. How many grams remain after 6 hours? b. What is the half life substance? c. How       Log On


   

Question 374179: A radioactive substance decats by 5% every hour. Intially rhere are 500g of substance.
a. How many grams remain after 6 hours?
b. What is the half life substance?
c. How long will it take the 500g to decay to 200g?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
The equation to use is x%28t%29+=+500e%5E%28-0.05t%29.
a.++x%286%29+=+500e%5E%28-0.05%2A6%29+=+500e%5E-0.3+=+370.409grams.
b. 250+=+500e%5E%28-0.05t%29, 0.5+=+e%5E%28-0.05t%29, which gives ln0.5+=+-0.05t, or t+=+ln0.5%2F-0.05+=+13.86 hours.
c. 200+=+500e%5E%28-0.05t%29 implies that 0.4+=+e%5E%28-0.05t%29, or ln0.4+=+-0.05t, or t+=+ln0.04%2F-0.05+=+18.33 hours.