Question 1130378: A laboratory has a 750g sample of uranium. This substance has a half life of 20 years.
a) Write an equation to represent the mass of the substance after x half lives.
b) how many half-lives will have elapsed in 120 years ?
c) How much of the sample is left after 120 years?
Thank you
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
Part A
Start off with 750 grams of the material. After 1 half-life, you have 750*(1/2) = 375 grams. After 2 half-lives, you have 750*(1/2)*(1/2) = 187.5 grams. This pattern continues. The number of half-lives determines how many copies of (1/2) you will multiply.
If there were 5 copies of (1/2), then this refers to 5 half-lives. We can write it as (1/2)*(1/2)*(1/2)*(1/2)*(1/2) or we can use exponentials as a shortcut and say (1/2)^5
If there are x half-lives that occur, then we multiply by (1/2)^x
Therefore, the equation is y = 750*(1/2)^x where x is the number of half-lives and y is the amount of material remaining.
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Part B
"A half life of 20 years" means that every 20 year mark has the amount of uranium cut in half. Refer to part A.
Divide 120 over 20 to get 120/20 = 6.
There are 6 half-lives in 120 years.
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Part C
From part B, we found that 120 years is 6 half-lives for this material, so x = 6.
Plug x = 6 into the equation found in part A. Use the order of operations PEMDAS to simplify.
y = 750*(1/2)^x
y = 750*(1/2)^6 .... replace x with 6
y = 750*(0.5)^6
y = 750*0.015625
y = 11.71875
There is 11.71875 grams of uranium left after 120 years.
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