In Exercises a medical researcher wants to determine the concentration C (in moles per liter) of a tracer drug injected into a moving fluid. Solve this problem by considering a single-compartment dilution model (see figure). Assume that the fluid is continuously mixed and that the volume of the fluid in the compartment is constant.

If the tracer is injected instantaneously at time t = 0, then the of concentration of the fluid in the compartment begins diluting
according to the differential equation

where C = C₀ when t = 0. 

(a) Solve this differential equation to find the concentration C as a function of time t. 

(b) Find the limit of C as t → ∞.

Transcribed Image Text:

Tracer injected Flow R (pure) Volume V Flow R (concentration C)