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.
