Answer
a. $C(40)\approx86.67$ million dollars for $40\%$ inoculation, $C(80)=520$ million dollars for $80\%$ inoculation, and $C(90)=1170$ million dollars for $90\%$ inoculation.
b. $x=100(\%)$
c. See explanations.
Work Step by Step
a. Given the formula of the cost as $C(x)=\frac{130x}{100-x}$, we have $C(40)=\frac{130(40)}{100-(40)}=\frac{260}{3}\approx86.67$ million dollars, which is the cost to inoculate $40\%$ of the population against the flu. Similarly, we have $C(80)=\frac{130(80)}{100-(80)}=520$ million dollars for $80\%$ inoculation, and $C(90)=\frac{130(90)}{100-(90)}=1170$ million dollars for $90\%$ inoculation (drastic increases).
b. The expression will be undefined if the denominator is zero, which happens at $100-x=0$ or $x=100(\%)$
c. When $x\to 100, C(x)\to \infty$, which means that the cost will increase rapidly when $x$ gets closer to $100$. In other words, it is not possible to inoculate $100\%$ of the population.
