# Math Help - Decay

1. ## Decay

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?

2. 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.