Tin decay using separable equ's

[jenettezone]

Homework Statement

A tin organ pipe decays with age as a result of a chemical reaction that is catalyzed by the decayed tin. as a result, the rate at which the tin decays is proportional to the product of the amount of tin left and the amount that has already decayed. Let M be the total amount of tin left before any has decayed. Find the amount of decayed tin p(t).

Homework Equations

"Find the amount of decayed tin p(t)." → p(t)=decayed tin,

"Let M be the total amount of tin left before any has decayed." → amount of tin left=M-p(t)?

The Attempt at a Solution

"the rate at which the tin decays is proportional to the product of the amount of tin left and the amount that has already decayed." → dp/dtαM-p(t)αp(t)

I am not sure if my interpretation of the data is correct. or if it is, i do not know what to do with it to get an equation for p(t). please help!

 

[kuruman]

Let q(t) = amount of tin left. Then
M-q(t) = amount of tin decayed and
q(t)*(M-q(t))=product of amount left and amount already decayed.

Can you write a differential equation saying "the rate at which the tin decays is proportional to the product of the amount of tin left and the amount that has already decayed"?