Question

both anibiotics were prescribed in high dosage clow release capsules. Th efunctions C(x) = 5log(x+1)+10 models the concentration of levofloxacin in mol/L over a time x, in hours the function c(x)=5log(x+1)+10 models the concentration of levofloxcin and metrinidazole.

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) fiffer from the individual graphs of C(x) and D(x)? Explain.

Answer 1

hard to answer the questions, since you left out d(x)
(a) initial concentration is just the constant term, since log(1)=0
(b) when c(x)=d(x) the concentrations are equal (duh) Just solve for x to find when that is.
(c) (c+d)(x) = c(x)+d(x)

Answer 2

The first part is wrong; it should be.....

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 c(x)=5log(x+1)+10 models the concentration of levofloxcin and metrinidazole in mol/L over time x, in hours.

Answer 3

I rewrote it so it would make more sense...

The function D(x)=5log(x+1)+10 models the concentration of levofloxcin and metrinidazole in mol/L over time x, in hours.

Answer 4

huh.
still looks like C and D are the same model.

Answer 5

i keep making typos
its supposed to be D(x)= 10log(x+1) + 5.

Answer 6

well, I gave you some hints. I'll do (b) because (a) should be trivial

5log(x+1)+10=10log(x+1)+5
dividing by 5,
log(x+1)+2=2log(x+1)+1
log(x+1)=1
x+1 = 10
x = 9

see what you can do with the other parts.

Answer 7

I already got a and b and I got the same answer.

Answer 8

for c), i graphed to (C+D)(x), C(x) and D(x) and found that they all are pretty similar. Wouldn't the only difference be that (C+D)(x) has a greater concentration after x amount of hours?

Answer 9

yes, since the graph of (c+d)(x) is the sum of the graphs of c(x) and d(x). I mean, geez, that's what "+" means...