Question

1) The rational function shown could be used to the number of arrests, f(x), per 100,000 drivers, for driving under the influence of alcohol, as a function of a driver’s age, x.
$f(x)=\frac{27725(x-14)}{x^2+9} -5x$

a) Describe the trend you see in the graph, in context.
b)Use a graphing utility to determine the age that corresponds to the greatest number of arrests.

Answer 1

The age that has the maximum number of arrest is 25 years

The trend on the graph

The equation of the function is given as:

$f\left(x\right)\ =\ \frac{27725\left(x\ -\ 14\right)}{x^{2\ }+\ 9}-5x$

See attachment for the graph of the function.

The end behavior of the graph is

$\mathrm{as}\:x\to \:+\infty \:,\:f\left(x\right)\to \:-\infty \:,\:\:\mathrm{and\:as}\:x\to \:-\infty \:,\:f\left(x\right)\to \:+\infty \:$

This means that:

As the age of the driver increases, arrested drivers decreases and as the age of the driver decreases, arrested drivers increases

The age that has the maximum arrest

From the graph, the maximum is:

Maximum = (25.388, 356.166)

Remove the y values

Maximum = 25.388

Approximate

Maximum = 25

Hence, the age that has the maximum arrest is 25

Read more about functions at:

brainly.com/question/23426439

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