The surge function C(t)=10te^(-t) is used to model response to an initial dose of medication which rises rapidly and reaches a maximum thereafter, the drug begins to decay and leave the bloodstream. The domain for the surge function C(t)=10te^(-t) is given as 0≤t≤4. The function 10te^(-t)+10(t-4)e^(-(t-4)) is a surge function but it models when the second dose of medication should be administered and where it would be effective. After four hours, a patient takes a second dose of Voltar.
Explain why the concentration of the medication Voltar in the patient’s system can be given by:
C = 10xe^-x
C = 10xe^-x + 10 (x - 4)e^-(x-4)