Answer:
(a)
(b)
Step-by-step explanation:
Given
--- Volume of tank
--- Brine solution
--- Rate in, in gallon/min
--- Rate out, in gallon/min
Required
Determine A(t)
First, calculate the rate in (R in) and (R out) in lb/min
R(out) is calculated by multiply the rate at which brine leaves the tank (lb/gal) * R2
So, we have:
The change in the amount of brin e in the tank at time t is given as:
Rewrite:
Multiply through by dt
Make dt stand alone
Express as exponents
Multiply through by 100
Apply initial conditions
Substitute 0 for t in:
Substitute 15 for c in
Factorize:
How long to empty the tank
Set A to 0
Divide through by 1500
Collect Like Terms
Take ln of both sides