Science:Math Exam Resources/Courses/MATH100 B/December 2023/Question 30(a)/Statement

A drug used to treat cancer is effective at low doses with an efficacy (ability to cure) that increases with the quantity of the drug used for treatment. However, at sufficiently high doses, the drug becomes toxic (can cause death). The fraction of patients surviving cancer with this drug treatment is given by

$$S(x)={\frac {x}{k_{1}+x}}-{\frac {x}{k_{2}+x}}$$

where ${\textstyle x}$ is the drug quantity in hundreds of milligrams/day given to the patient and ${\textstyle 0<k_{1}<k_{2}}$.

(a) Find ${\textstyle S(0)}$. Explain what your finding means in medical terms.