# A Real-life Application of Rational Functions

Describe the cost C(x), in millions of dollars to inoculate x % of the Canadian population against a particularly virulent strain of flu

C(x)=130x

____

100-x

a) sketch the rational function showing only the regions of the curve that are relevant in the context of this problem (ie. an appropriate domain)

b) explain the behavior of the function around its vertical asymptote using the appropriate mathematical symbols. Explain what this asymptote represents in the context of this problem

c) In order to reasonably utilize the available health care resources a decision on a cost-benefits basis must be made as the % of the population that will be inoculated. What is a reasonable percentage? Explain and justify your decision.

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#### Solution Preview

C(x)=130x/(100-x)

a) sketch the rational function showing only the regions of the curve that are relevant in the context of this problem (ie. an appropriate domain)

The graph of the function is a hyperbola. It only makes sense to skatch a graph for 0<x<100

b) explain the behavior of the function around its vertical asymptote using the appropriate mathematical symblos. explain what this asymptote represents in the context of this problem.

The vertical asymptote is at x=100 since the denominator 100-x is 0 when x=100

As x ->100 from the left (x<100), f(x) -> âˆž ...

#### Solution Summary

A function is described in terms of a real-life problem.