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.

Question

A) Which of the two drugs has a higher initial concentration in the blood
stream? Justify your answer with an explanation.

B)Determine when C(x)=D(x) algebraically and state what this
represents in this situation.

C)If Mathews is instructed to take both antibiotics at once the
concentration levels could be modeled by the function (C+D)(x) . How would the graph of (C+D)(x) differ from the individual graphs of C(x) and D(x)? explain.

Answer 1

(A) what are the values when t=0?
(B) so do the math
5log(x+1)+10 = 10log(x+1)+5
log(x+1) = 1
now finish it off
(C) the graph of (C+D)(x) is just the sum of C(x)+D(x)

Answer 2

there is no value for t

Answer 3

oh, well, duh. then when x=0