estimate the waiting time if the width is increased to 26ft and R decreases to .19

To estimate the pedestrian's waiting time with the new conditions:

- \( w = 26 \) feet
- \( R = 0.19 \) vehicles per second

we'll use the provided formula:

\[
f(w, R) = \left(\frac{w}{3.4}\right) e^{wR/3.4}
\]

### Step-by-Step Calculation

1. **Compute \(\frac{w}{3.4}\):**

   \[
   \frac{26}{3.4} \approx 7.6471
   \]

2. **Compute the exponent:**

   \[
   \frac{26 \times 0.19}{3.4} = \frac{4.94}{3.4} \approx 1.4529
   \]

3. **Calculate the exponential term \(e^{1.4529}\):**

   \[
   e^{1.4529} \approx 4.273
   \]

4. **Calculate the waiting time:**

   \[
   f(26, 0.19) \approx 7.6471 \times 4.273 \approx 32.68
   \]

### Result

The estimated waiting time for a pedestrian when the road width is increased to 26 feet and the vehicle rate decreases to 0.19 vehicles per second is approximately **32.68 seconds**.

### Additional Considerations

- The waiting time is sensitive to changes in both width and vehicle rate. Increasing the width or decreasing the vehicle rate can significantly affect the waiting time.
- Exponential growth in the formula suggests that small changes in parameters can have a large impact, which should be considered when evaluating traffic scenarios.

### Questions You Might Have

1. Would you like to see how different widths or rates affect waiting time further?
2. Do you need a detailed explanation of the exponential function used in this context?
3. Are there any other specific parameters you'd like to test?
4. How does changing the vehicle rate affect waiting times compared to changes in width?
5. Would you like to explore similar problems with different speeds for pedestrians?

### Tip

When estimating waiting times with exponential functions, always pay attention to the base of the exponential term, as it can lead to rapid changes in the output with even minor adjustments in the inputs.

Learn how to estimate the waiting time for pedestrians with a road width increased to 26 feet and a vehicle rate decreased to 0.19 vehicles per second using the exponential growth formula. Explore the sensitivity of waiting time to changes in width and vehicle rate.

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