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.
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.
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To understand how the graph of (C + D)(x) differs from the individual graphs of C(x) and D(x), let's first look at what each function represents.
The function C(x) = 5log(x+1) + 10 represents the concentration of levofloxacin in mol/L over time x. This means that if we plug in a value for x, the output of the function will give us the concentration of levofloxacin at that particular time. The function D(x) = 10log(x+1) + 5 represents the concentration of metronidazole in mol/L over time x. Similarly, plugging in a value for x into this function will give us the concentration of metronidazole at that time.
Now, when we take both antibiotics at once, we can model the combined concentration levels using the function (C + D)(x). The (C + D)(x) function simply represents the sum of the concentration of levofloxacin and metronidazole at each time x. Mathematically, it can be represented as (C + D)(x) = C(x) + D(x).
Graphically, if we were to plot the individual graphs of C(x) and D(x) on the same coordinate system, we would see two separate lines representing the concentration changes of levofloxacin and metronidazole over time. However, when we graph (C + D)(x), we would get a single curve that represents the combined concentration levels of both antibiotics.
The difference lies in the fact that (C + D)(x) takes into account the concentrations of both antibiotics and gives us the combined concentration. This can be useful for understanding the overall effect of taking both antibiotics together, as the combined concentration levels may have different implications compared to the individual concentrations.