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 $A_0$.
_______________________________________________

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

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

There are currently 1 users browsing this thread. (0 members and 1 guests)

#### Posting Permissions

• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts
•