Thread: Natural decay question

1. Natural decay question

twenty grams of salt is gradually dissolved in hot water. assume that the amount S left I dissolved after t minutes satisfies the law of natural decay dS/dt = -kS for some positive constant k.

Show that S = 20e^-kt

2. Re: Natural decay question

We may assume that if

$\frac{dA}{dt} = kA$

then

$A = A_0 e^{kt}$

for some constant $A_0$.
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Applying this to your question:

$\frac{dS}{dt} = -kS \implies S = S_0e^{-kt}$

and we know the initial amount of salt to be 20 grams, that is, $t=0,\,S=20$. $S_0$ must then be equal to $20$.

Therefore, $S =20e^{-kt}$.

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