Answer to Question #272703 in Algebra for NABTAB

Question

Polynomial and rational functions can be used to model a wide variety of phenomena of science, technology, and everyday life.

Go to www.desmos.com/calculator, write your equation, or function, and develop your explanation using the properties of graphs.

Your Discussion should be a minimum of 250 words in length and not more than 750 words

Answer 1

Rational functions can be applied to many real-life applications. Take for instance, the

Potency of a drug and its pain-relieving effects on the body at (t) hours are expressed

by the function $P(t)=\frac{4t}{3t^2+3}$ . This is a rational function, as it is a ratio of two

polynomial functions (4t) and$(3t^2+3)$ . (4t) is a polynomial because it can be expressed

as (4t+0).

$P(t)=\frac{4t}{3t^2+3}$

For 1 hour $P(t)= \frac{4(1)}{3(1)^2+3}=4/6$ or 66% potency.

For 2 hour $P(t)= \frac{4(2)}{3(2)^2+3}=8/15$ 0r 53% potency.

For 4 hour $P(t)=\frac{4(4)}{3(4)^2+3}=16/51$ or 31% potency.

This pain reliever gives you the most pain fighting strength by the first hour with a 66

percent potency. After hour 2, the potency drops to 53 percent. The drugs power

gradually decreases by hour 8, tapering down to about 15 percent. Pain medications

commonly ware off after 4 to 6 hours. All drugs are evaluated in this fashion to rate their

strength and potential harm to the person taking them. It is crucial to the health of the

public to accurately assess all drugs potency and recommended dosages