Multi-variable functions and Physical Interpretation

Question

Given the function where x, is measured in milligrams, and t is in hours. $$C(x,t)=0.2x(e^{-0.2t}-e^{-t})$$

I have to find the value of the function at the following x, and t values: $C(23,5)$.

I did the work for the problem and had to round it to two decimal places. To get $1.66\mathrm{\frac{mg}{L}}$ as $C(23,5)$ I also have to find out the physical context of my answer.

Is this the correct physical context?

At an initial dosage of $23 \ \mathrm{mg}$ at the 5th hour the concentration of said dosage will be diminished to approximately $1.66 \ \mathrm{\frac{mg}L}$

Answer 1

First off, you want to avoid the term "initial" in your explanation as the typical interpretation of that word means $t = 0$. In this case:

$$C(x, 0) = 0$$

No matter what dosage is given, there is zero concentration in the system at the "initial" state. That being said, I think if you remove that and rephrase your explanation to something like

A dosage of 23 mg yields a concentration of 1.66 mg/L after 5 hours.

It would be understood well. Hope that was helpful!