The average number of vehicles waiting in line to enter a sports arena parking lot is modeled by the function $W(x)=\frac{x^{2}}{2(1-x)}$, where $x$ is a number between 0 and 1 known as the traffic intensity. For each traffic intensity, find the average number of vehicles waiting.
(a) 0.1
(b) 0.5
(c) 0.6
(d)What happens to waiting time as traffic intensity increases?
(a) The average number of vehicles waiting in line is approximately
(Type an integer or a decimal rounded to the nearest tenth as needed.)

Step 1 ：Substitute \(x = 0.1\) into the function \(W(x)\):

Step 2 ：\(W(0.1) = \frac{(0.1)^2}{2(1 - 0.1)}\)

Step 3 ：Calculate the numerator: \((0.1)^2 = 0.01\)

Step 4 ：Calculate the denominator: \(2(1 - 0.1) = 1.8\)

Step 5 ：Divide the numerator by the denominator: \(\frac{0.01}{1.8} = 0.0056\)

Step 6 ：\(\boxed{W(0.1) = 0.0056}\)

Step 7 ：Substitute \(x = 0.5\) into the function \(W(x)\):

Step 8 ：\(W(0.5) = \frac{(0.5)^2}{2(1 - 0.5)}\)

Step 9 ：Calculate the numerator: \((0.5)^2 = 0.25\)

Step 10 ：Calculate the denominator: \(2(1 - 0.5) = 1\)

Step 11 ：Divide the numerator by the denominator: \(\frac{0.25}{1} = 0.25\)

Step 12 ：\(\boxed{W(0.5) = 0.25}\)

Step 13 ：Substitute \(x = 0.6\) into the function \(W(x)\):

Step 14 ：\(W(0.6) = \frac{(0.6)^2}{2(1 - 0.6)}\)

Step 15 ：Calculate the numerator: \((0.6)^2 = 0.36\)

Step 16 ：Calculate the denominator: \(2(1 - 0.6) = 0.8\)

Step 17 ：Divide the numerator by the denominator: \(\frac{0.36}{0.8} = 0.45\)

Step 18 ：\(\boxed{W(0.6) = 0.45}\)

Step 19 ：As the traffic intensity increases, the denominator of the function \(W(x)\) decreases (since \(1 - x\) decreases as \(x\) increases). Since the numerator (\(x^2\)) increases as \(x\) increases, the overall value of the function \(W(x)\) increases as \(x\) increases. Therefore, as the traffic intensity increases, the average number of vehicles waiting in line also increases.