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.
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.
Answers
Steve
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)
(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)
Anonymous
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.
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.
Anonymous
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.
The function D(x)=5log(x+1)+10 models the concentration of levofloxcin and metrinidazole in mol/L over time x, in hours.
Steve
huh.
still looks like C and D are the same model.
still looks like C and D are the same model.
Anonymous
i keep making typos
its supposed to be D(x)= 10log(x+1) + 5.
its supposed to be D(x)= 10log(x+1) + 5.
Steve
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.
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.
Anonymous
I already got a and b and I got the same answer.
Anonymous
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?
Steve
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...