A radioactive element's half-life is the time it takes for one half of the element's quantity to decay. The half=lif of Plutonium-241 is 14.4 years. The number of grams A of Plutonium-241 left after t years can be modeled by A = p(0.5) t/14.4, where p is the original amount of the element.
a. How much of a 0.2-gram sample remains after 72 years?
b. How much of a 5.4-gram sample remains after 1095 days?
I would like very detailed explanations on how to do this, after all, I want to learn, not just know the answer. Thankyou :)
I'll give 5 stars for detailed explanations :)
a. A = p(0.5) t/14.4 {THIS FORMULA IS WRONG THE WAY YOU HAVE WRITTEN}. I believe it should be written like this: A=p*.5^(t/14.4), then we have:
A=.2*.03125=0.00625 grams left after 72 years.
b. A=5.4*.5^(3/14.4)=4.674 grams left after 1,095 days or exactly 3 years.
DETAILED CALCULATION OF a.
A=.2 X [.5^(t/14.4)]=.2 X [.5^(72/14.4)]=.2 X [.5^5]=.2 X 0.03125=.00625, which is the answer for a. Now do exactly the same thing for b. Remember to convert days into years:1,095/365=3 years.
