$[15]$ A simple model for the flow between permeable membranes is represented by the following

diagram.

The transport in all directions is at the same rate as represented by the arrows to the left and right.

That is $AB,2m^{-1},BA2m^{-1}$ and all reservoirs $A,B$ and $C$ are the same size.

$AC2m^{-1},CA2m^{-1}$

Reservoir A contains $60g$ of salt dissolved in fresh water at time $t=0.$ Side B and C contain $0g$ of salt

at time $t=0.$

Show all steps for the following questions

a$.$ Setup the system of equations that model this system.

b$.$ Using the Laplace transform method to find $A(t),B(t)$ and $C(t),$ that is the amounts of salt in each

respectively as a function of time.

c$.$ Using the answer found in part $b.$ for $A(t),B(t)$ and $C(t)$ show what happens as $t?$

What can you say about these values?