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.
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)
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.
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.
huh.
still looks like C and D are the same model.
i keep making typos
its supposed to be D(x)= 10log(x+1) + 5.
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.
I already got a and b and I got the same answer.
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?
a) To determine which drug has a higher initial concentration in the bloodstream, we can compare the values of C(x) and D(x) at x = 0. Plug in x = 0 into both functions.
For C(x) = 5log(x+1)+10, substituting x = 0 gives C(0) = 5log(0+1) + 10 = 5log(1) + 10 = 5(0) + 10 = 10.
For D(x), the equation is not given, so we cannot directly determine its value at x = 0. However, if we assume that the initial concentration of metronidazole is the same as levofloxacin (which is a reasonable assumption since they are prescribed in the same dosage), then we can assume the initial concentration of D(x) is also 10 mol/L.
Since both C(x) and D(x) have the same initial concentration of 10 mol/L, neither drug has a higher initial concentration in the bloodstream.
b) To determine when C(x) = D(x), we can set the two functions equal to each other and solve for x algebraically.
5log(x+1) + 10 = D(x)
Since the equation for D(x) is not given, we cannot solve this equation without knowing the specific equation for D(x). We would need more information to complete this part of the question.
c) If (C + D)(x) represents the concentration levels of both antibiotics taken at once, the graph of (C + D)(x) would be a combination of the individual graphs of C(x) and D(x).
Mathematically, (C + D)(x) can be represented as (5log(x+1) + 10) + D(x). When both functions are added together, the resulting graph would show the combined concentration levels of both drugs over time.
The graph of (C + D)(x) would generally have higher concentration values compared to the individual graphs of C(x) and D(x) since we are adding the concentrations of both drugs at each time point. Additionally, the shape and behavior of the graph would depend on the specific equations for C(x) and D(x), which are not provided in the question.