## Related questions with answers

In this exercise, 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 singlecompartment dilution model. 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 concentration of the fluid in the compartment begins diluting according to the differential equation

$\dfrac{dC}{dt}=\left(-\dfrac{R}{V}\right)C,\quad C=C_0$ when $t=0$.

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

Solution

Verified**(a)**

Solving the differential equation to find the concentration $C$ as a function of $t$:

$\begin{aligned} \dfrac{dC}{dt} &= \left(-\dfrac{R}{V}\right)C \end{aligned}$

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