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goblinko [34]
4 years ago
13

Please help me answer this. My professor taught us this but with the formula on the right.

Mathematics
1 answer:
ASHA 777 [7]4 years ago
3 0
First lets rearrange the formula to solve for half-life.
The half-life is the time it takes for half of the element to decay.
e^{rt} = \frac{1}{2}   \\ t = \frac{ln (\frac{1}{2})}{r}

So now we need to find "r" which is the rate of decay.
If we rearrange formula to solve for r:
P e^{rt} = A  \\  \\  r = \frac{ln (\frac{A}{P})}{t}

Substituting this into equation for half-life, you get:
T = (\frac{ ln (1/2)}{ln (A/P)} ) t = \frac{ ln(1/2)}{ln (200/500)} *(48) = 36.31
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