Chapter 4.5, Problem 38E

Analysis of the Effectiveness of an Insect Repellent Human hands covered with cotton fabrics impregnated with the insect repellent DEPA were inserted for $5$ minutes into a test chamber containing $200$ female mosquitoes. The function $f(x)=26.48-14.09\ln x$ gives the number of mosquito bites received when the concentration was $x$ percent. [Note: The answers to parts $(b)-(e)$ can be obtained either algebraically or from the graphs. You might consider trying both methods.] (Source:Journal of Medical Entomology.)

a. Graph $f(x)$ and $f\text{'}(x)$ for $0<x\le 6$.

b. How many bites were received when the concentration was $3.25\%$?

c. What concentration resulted in $15$ bites?

d. At what rate is the number of bites changing with respect to concentration of DEPA when $x=2.75$?

e. For what concentration does the rate of change of bites with respect to concentration equal $-10$ bites per percentage increase in concentration?