Question

Sarah is fighting a sinus infection. Her doctor prescribed a nasal spray and an antibiotic to ght the infection. The active ingredients, in milligrams, remaining in the bloodstream from the nasal spray, n(t), and the antibiotic, a(t), are modeled in the functions below, where t is the time in hours since the medications were taken.

Answer 1

The antibiotics has greater initial amount of active ingredient.

Step-by-step explanation:

Okay, from the question we are given the equation for the medication formula for the Nasal spray and the antibiotics, they are given as equation (1) and (2) respectively;

n(t) = [ (t + 1) / (t + 5) ] + [18 / (t² + 8t + 15) ]. -----------------------------------------(1).

a(t) = 9 / (t+3) ----------------------------(2).

Immediately Sarah used the drug, let us say time,t = 0 is the time in which active ingredients(in milligrams) are much more concentrated in the bloodstream of Sarah.

Therefore at t =0, we are going to have;

n(0) = [ (0 + 1) / (0+ 5) ] + [18 / (0 + 8(0) + 15) ].

n(0) = (1/5 + 18/15).

n(0) = 1.4.

Also, for the antibiotics, the concentration at time,t = 0 is;

a(t) = 9 / (t+3).

a(0) = 9/ 0 + 3 = 9/3 = 3.

a(0) = 3.

The values of the Nasal spay is lesser than that of the value of the antibiotics, therefore we can come to conclusion that "The antibiotics has greater initial amount of active ingredient''.