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## teller one year ago 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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1. anonymous

$A=A_0\cdot \left( \frac{ 1 }{ 2 } \right)^k$where $$A_0$$ is the initial amount $$A$$ is the amount remaining after k half-lives and k is the number of half-lives

2. teller

So 165=3*(1/2)^k?

3. anonymous

no... A = 165*(1/2)^3

4. teller

165/8?

5. anonymous

yep

6. teller

but it has to be rounded to the nearest gram how do I do that? It can't be in fraction form.

7. anonymous

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

8. teller

divide it by what do I divide 165 by 8?

9. anonymous

yes, that is another way to represent 165/8

10. teller

I got 20.625 is that right?

11. anonymous

does that make sense to you? what is 20 * 8?

12. teller

160

13. anonymous

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?

14. anonymous

so final answer, rounded to the nearest gram?

15. teller

I'm confused at what I'm supposed to be rounding...

16. anonymous

20.625

17. teller

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.

18. teller

I got that but how do I round that?

19. anonymous

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. teller

20

21. teller

no wait 21

22. anonymous

there you go!

23. teller

so 20.621?

24. anonymous

?

25. teller

you said 21 so 20.621

26. anonymous

no... to the nearest gram... no numbers after the decimal!!!

27. teller

oh okay thank you

28. teller

Mind helping me with another one?

29. anonymous

i would but i'm heading out. going for a bike ride. good luck!

30. teller

Alright thanks

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