Decay

**CalcQueen** · March 11th 2009, 06:07 AM

Suppose the decay for a radioactive element is known to be y=y e^-0.24t, with t in years. About how long will it take for a sample of this element to decay to 70% of its original amount?

**mr fantastic** · March 11th 2009, 06:43 AM

Originally Posted by CalcQueen

Suppose the decay for a radioactive element is known to be y=y e^-0.24t, with t in years. About how long will it take for a sample of this element to decay to 70% of its original amount?

I assume you mean $y = {\color{red}y_0} e^{-0.24t}$ .

The initial amount is $y_0$ . So substitute $y = 0.7 y_0$ and solve for $t$ :

$0.7 y_0 = y_0 e^{-0.24t} \Rightarrow 0.7 = e^{-0.24t}$ etc.

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