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.

Question

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.

anonymous · Answer

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

teller · Answer

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

anonymous · Answer

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

teller · Answer

165/8?

anonymous · Answer

yep

teller · Answer

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

anonymous · Answer

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

teller · Answer

divide it by what do I divide 165 by 8?

anonymous · Answer

yes, that is another way to represent 165/8

teller · Answer

I got 20.625  is that right?

anonymous · Answer

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

teller · Answer

160

anonymous · Answer

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?

anonymous · Answer

so final answer, rounded to the nearest gram?

teller · Answer

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

anonymous · Answer

20.625

teller · Answer

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.

teller · Answer

I got that but how do I round that?

anonymous · Answer

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?

teller · Answer

20

teller · Answer

no wait 21

anonymous · Answer

there you go!

teller · Answer

so 20.621?

anonymous · Answer

?

teller · Answer

you said 21 so 20.621

anonymous · Answer

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

teller · Answer

oh okay thank you

teller · Answer

Mind helping me with another one?

anonymous · Answer

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

teller · Answer

Alright thanks