The concentration c (in mg/dl), of an antibiotic in a patient’s bloodstream per hour, t, is given by: c(t) = (50t)/(t^2+25) in order for the antibiotic to be effective, 4 or more mg/dl must be present in the bloodstream. when do you have to take the antibiotic after the initial dose? solve algebraically and graphically.

Step-by-step explanation:

Functions

The problem describes a function that expresses the concentration of an antibiotic in mg/dl vs time in hours as:

We need to find the first value of t such that

It means that

Operating with the inequality

Rearranging and dividing by 2, we have a polynomial inequality:

Factoring

There are two possible values for t, both valids because they are positive

We need to find the first value, i.e.

Now for the graphic method, we plot the graph for the function and a horizontal line at c=4 to find the values of t.

The graph is shown in the image provided below. We can see both values where the funcion and C=4 intersect. Both values coincide with the previously analitically found values

step-by-step explanation:

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