Hi, I was just wondering how one would arrive at the answers to these questions. I have the solution for parts a and b, but not for part c.(adsbygoogle = window.adsbygoogle || []).push({});

Suppose that antibiotics are injected into a patient to treat a sinus infection. The antibiotics circulate in the blood, slowly diffusing into the sinus cavity while simultaneously being filtered out of the blood by the liver. A model for the concentration of the antibiotic in the sinus cavity as a function of time since the injection:

c(t) = [e^(−αt) − e^(−βt)]/ β − α

Where β > α > 0.

(a) At what time does c have its maximum value?

SOLUTION: t = [ln(α) − ln(β)] / α - β

I know that to be a maximum value the t would need to be solved with the use of: c^{1}(t)>0 , as well as the fact that natural log rules can be applied to this equation to make differentiation easier. But I have no idea how to get there and achieve the final answer.

(b) At what time does the inflection point occur?

SOLUTION: t = 2[ln(α) − ln(β)] / α - β

I do know that for a point of inflection c^{2}(t)=0, as well as the fact that the same application of natural log rules would apply for this problem. But I don't know how to apply this for this problem.

(c) what would the graph of c look like?

*attached picture shows options..

I did come to the conclusion that it has to be one of the top two graphs, but I don't know which one/why.

Any help would be much appreciated! :)

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# I Help please with biocalculus question involving differentiation

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