Can someone please help me ? The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with 165 grams of a radioactive isotope, how much will be left after 3 half-lives?Use the calculator provided and round your answer to the nearest gram.

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Can someone please help me ? The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with 165 grams of a radioactive isotope, how much will be left after 3 half-lives?Use the calculator provided and round your answer to the nearest gram.

Algebra
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\[A=A_0\cdot \left( \frac{ 1 }{ 2 } \right)^k\]where \(A_0\) is the initial amount \(A\) is the amount remaining after k half-lives and k is the number of half-lives
So 165=3*(1/2)^k?
no... A = 165*(1/2)^3

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165/8?
yep
but it has to be rounded to the nearest gram how do I do that? It can't be in fraction form.
divide and see what you get... the problem says to use the calculator provided but any calculator will work... or you can use long division
divide it by what do I divide 165 by 8?
yes, that is another way to represent 165/8
I got 20.625 is that right?
does that make sense to you? what is 20 * 8?
160
so let's rewrite: \[\frac{ 20\cdot 8 }{ 8}+\frac{ 5 }{ 8 }=\frac{ 160 }{ 8 }+\frac{ 5 }{ 8 }=\frac{ 165 }{8}\]and 5/8 is less than 1 but more than 1/2 = .5, correct?
so final answer, rounded to the nearest gram?
I'm confused at what I'm supposed to be rounding...
20.625
But how do I do that I already did that and I gave you the answer but you never told me if it was right.
I got that but how do I round that?
20.625 is not rounded to the nearest gram... 20.625 grams is the exact answer but they want the answer rounded to the nearest gram. which is closer to 20.625... 20 or 21?
20
no wait 21
there you go!
so 20.621?
?
you said 21 so 20.621
no... to the nearest gram... no numbers after the decimal!!!
oh okay thank you
Mind helping me with another one?
i would but i'm heading out. going for a bike ride. good luck!
Alright thanks

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