3

Given the information you provided:

1. **August Usage**:
   - Forecasted: 88% of capacity
   - Actual: 89.6% of capacity
   - Smoothing constant: 0.10

Let's calculate the forecast for September and October:

a. **Forecast for September**:
   - Forecast for September = Previous Forecast + Smoothing Constant * (Actual August - Previous Forecast)

   Forecast for September = 88 + 0.10 * (89.6 - 88)
   Forecast for September = 88 + 0.10 * 1.6
   Forecast for September = 88 + 0.16
   Forecast for September = 88.16

   So, the forecasted usage for September is 88.16% of capacity.

b. **Forecast for October**:
   - Actual: 43% of capacity
   - Smoothing constant: 0.10

   Now, we'll use the forecasted value from September to predict the October usage:

   Forecast for October = Forecast for September + Smoothing Constant * (Actual September - Forecast for September)

   Forecast for October = 88.16 + 0.10 * (43 - 88.16)
   Forecast for October = 88.16 - 4.487
   Forecast for October ≈ 83.67

   The forecasted usage for October is approximately 83.67% of capacity.

Keep in mind that exponential smoothing provides a method of incorporating recent observations into the forecast, but it might not capture sudden changes or non-linear trends very effectively.