Question 1130378
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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, <font color=red>the equation is y = 750*(1/2)^x</font> 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 <font color=red>6 half-lives</font> 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 <font color=red>11.71875 grams</font> of uranium left after 120 years.
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