Help :(( Exponential Decay
a radio active element follows the law of exponential change and has a half-life of 38 hours. how long will it take for 90% of the radioactivity of the element to be dissipated ?
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Re: Help :((
Following exponential change
$x = x_o e^{-kt}$
After 38 hours, 50% is dissipated, hence 50% retained
$0.5x_o = x_o e^{-38k}$
$0.5 = e^{-38k}$
$e^{-k} = 0.5^{1/38}$
Thus,
$x = x_o 0.5^{t/38}$
90% dissipated means 10% retained, hence, x = 0.10xo
$0.10x_o = x_o 0.5^{t/38}$
$0.10 = 0.5^{t/38}$
$t = 126.23 ~ \text{hrs}$
Re: Help :(( Exponential Decay
You can also use exponential STAT in your calculator:
CASIO fx-991ES PLUS: [MODE] [3:Stat] [5:e^X]
[AC]
For 10% retained:
X (time) = 0.1x-caret = 126.23 hours
x-caret can be found at [Shift] [1:Stat] [5:Reg] [4:x-caret]