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The half-life of a radioactive element is defined as the amount of tim

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The half-life of a radioactive element is defined as the amount of tim  [#permalink]

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New post 25 Nov 2018, 07:02
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The half-life of a radioactive element is defined as the amount of time required for the amount of the element to decrease by half. If the half-life of an element is 3 years, how long will it take for the element to be reduced to one-eighth of its original amount?

A. 3 years
B. 9 years
C. 21 years
D. 24 years
E. 27 years
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Re: The half-life of a radioactive element is defined as the amount of tim  [#permalink]

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New post 25 Nov 2018, 11:51
rencsee wrote:
The half-life of a radioactive element is defined as the amount of time required for the amount of the element to decrease by half. If the half-life of an element is 3 years, how long will it take for the element to be reduced to one-eighth of its original amount?

A. 3 years
B. 9 years
C. 21 years
D. 24 years
E. 27 years

\(2M\,\,\mathop \to \limits^{3\,\,{\rm{years}}} \,\,M\)

\(8M\,\,\mathop \to \limits^{?\,\,{\rm{years}}} \,\,M\)


\(?\,\,\,\,:\,\,\,\,8M\,\,\mathop \to \limits^{3\,\,{\rm{years}}} \,\,4M\,\,\mathop \to \limits^{3\,\,{\rm{years}}} \,\,2M\,\,\mathop \to \limits^{3\,\,{\rm{years}}} \,\,M\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = 3 \cdot 3\,\,{\rm{years}}\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\left( {\rm{B}} \right)\)


This solution follows the notations and rationale taught in the GMATH method.

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Fabio.
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Re: The half-life of a radioactive element is defined as the amount of tim  [#permalink]

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New post 28 Nov 2018, 23:59
rencsee wrote:
The half-life of a radioactive element is defined as the amount of time required for the amount of the element to decrease by half. If the half-life of an element is 3 years, how long will it take for the element to be reduced to one-eighth of its original amount?

A. 3 years
B. 9 years
C. 21 years
D. 24 years
E. 27 years




Can someone provide more clarity on this problem? I am having trouble figuring this one out based on the half-life formula. Thx.
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Re: The half-life of a radioactive element is defined as the amount of tim &nbs [#permalink] 28 Nov 2018, 23:59
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The half-life of a radioactive element is defined as the amount of tim

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