Question #dd0a0

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Answer 1 · 2017-02-25T03:53:40

$\frac{1}{8}$ $1/8$

You can logic it out, or use the equation.

logic method

A half life is the time it takes for there to be half the amount. The total time is 72000 and the half life is 24000,

then there have been $\frac{72000}{24000} =$ $72000/24000 =$ 3 half-lives in this time.

Thus, a half of a half of a half = $\frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2}$ $1/2 * 1/2 *1/2$ = $\frac{1}{8}$ $1/8$ the original amount.

equation method

$Final Amount = Initial Amount \cdot {(0.5)}^{\frac{Time}{Half Life}}$ $"Final Amount" = "Initial Amount" * (0.5)^("Time"/"Half Life")$

$Final Amount = Initial Amount \cdot {(0.5)}^{3}$ $"Final Amount" = "Initial Amount" * (0.5)^3$

#"Final Amount" = 1/8"Initial Amount"

And so the fraction is $\frac{1}{8}$ $1/8$