The rational expression [tex]\frac{160 x}{100 - x}[/tex] describes the cost, in millions of dollars, to inoculate [tex]x[/tex] percent of the population against a particular strain of flu. Complete parts a through c.

a. Evaluate the expression for [tex]x = 40, x = 70[/tex], and [tex]x = 90[/tex]. Describe the meaning of each evaluation in terms of percentage inoculated and cost.

It costs [tex]$\[tex]$ \square[/tex] million to inoculate [tex]40 \%[/tex] of the population.

It costs [tex]$\$[/tex] \square[/tex] million to inoculate [tex]70 \%[/tex] of the population.

It costs [tex]$\$ \square[/tex] million to inoculate [tex]90 \%[/tex] of the population.

(Round to two decimal places as needed.)



Answer :

To evaluate the rational expression \(\frac{160x}{100-x}\) for \(x = 40\), \(x = 70\), and \(x = 90\) and describe the meaning of each evaluation in terms of percentage inoculated and cost, follow these steps:

1. Evaluating for \(x = 40\):
Substitute \(x = 40\) into the expression:
[tex]\[ \frac{160 \times 40}{100 - 40} = \frac{6400}{60} \approx 106.67 \][/tex]
So, it costs approximately $106.67 million to inoculate 40% of the population.

2. Evaluating for \(x = 70\):
Substitute \(x = 70\) into the expression:
[tex]\[ \frac{160 \times 70}{100 - 70} = \frac{11200}{30} \approx 373.33 \][/tex]
So, it costs approximately $373.33 million to inoculate 70% of the population.

3. Evaluating for \(x = 90\):
Substitute \(x = 90\) into the expression:
[tex]\[ \frac{160 \times 90}{100 - 90} = \frac{14400}{10} = 1440.00 \][/tex]
So, it costs approximately $1440 million to inoculate 90% of the population.

In summary:

- It costs \$106.67 million to inoculate 40% of the population.
- It costs \$373.33 million to inoculate 70% of the population.
- It costs \$1440 million to inoculate 90% of the population.