Both antibiotics were prescribed in high dosage slow release capsules. The function

C(x) = 5log(x +1) +10 models the concentration of levofloxacin in mol/L over a time x, in hours. The
function D(x) =10log(x+1)+5 models the concentration of metronidazole in mol/L over a time x, in hours. Which of the two drugs has a higher initial concentration in the blood stream? Justify your answer
with an explanation.

1 answer

To determine which drug has a higher initial concentration in the bloodstream, we need to compare the values of C(0) and D(0).

For C(x), the concentration of levofloxacin, we have:
C(0) = 5log(0 + 1) + 10 = 5log(1) + 10 = 5(0) + 10 = 10 mol/L

For D(x), the concentration of metronidazole, we have:
D(0) = 10log(0 + 1) + 5 = 10log(1) + 5 = 10(0) + 5 = 5 mol/L

Comparing these values, we can see that C(0) = 10 mol/L is higher than D(0) = 5 mol/L. Therefore, the drug levofloxacin has a higher initial concentration in the bloodstream compared to metronidazole.