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GuDViN [60]
3 years ago
13

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 o

rder 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.

Mathematics
1 answer:
NARA [144]3 years ago
4 0

Answer:

Step-by-step explanation:

<u>Functions </u>

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

\displaystyle c(t)=\frac{50\ t}{t^2+25}

We need to find the first value of t such that

\displaystyle c(t)\geq 4

It means that

\displaystyle \frac{50\ t}{t^2+25}\geq 4

Operating with the inequality

\displaystyle 50\ t\geq 4\ t^2+100

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

\displaystyle 2t^2-25t+50\leq 0

Factoring

\displaystyle 2(t-10)\left (t-\frac{5}{2}\right )\leq 0

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

\displaystyle t=\frac{5}{2}=2.5, \ t=10

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

t=2.5 \ hours

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

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Answer:

The number of units sold increased by \mathbf{11.2\%}

Step-by-step explanation:

Vacuum dealer sold units in 2011 = 420

Vacuum dealer sold units in 2012 = 467

We need to find percent increase or decrease

Since, In 2012 units sold are greater than 2011, so there will be percent increase.

The formula used is: Percent\:Increase=\frac{New\:Value-Original\:Value}{Original\:Value}\times 100

We have New Value (Units sold in 2012) = 467

Original Value (Units sold in 2011) = 420

Percent increase is:

Percent\:Increase=\frac{New\:Value-Original\:Value}{Original\:Value}\times 100\\Percent\:Increase=\frac{467-420}{420}\times 100\\Percent\:Increase=\frac{47}{420}\times 100\\Percent\:Increase=11.2\%

So, The number of units sold increased by \mathbf{11.2\%}

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3/x=y

Step-by-step explanation:

if not am sorry

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