Final answer:
The value for x_{t+1} in exponential smoothing is based on the previous data points with a formula using a smoothing constant, but the exact value cannot be provided without the specific smoothing equation or additional data.
Step-by-step explanation:
When using exponential smoothing for prediction/forecasting, the value used for x_{t+1} is an estimate based on the previous data points, but it's not directly provided in the question. Exponential smoothing leverages the formula that assigns a decreasing weight to older data points, with the most recent data point having the most significant influence. The actual calculation for the next value, x_{t+1}, would be based on the previous forecast and the smoothing constant applied to the most recent actual value of the series. Unfortunately, without additional context or the specific smoothing formula being referred to, it's not possible to provide the exact value or process for solving for x_{t+1}. This explanation applies to concepts such as time series analysis, statistical forecasting, and sales prediction, which are often included in college-level business, statistics, or mathematics courses.
When using exponential smoothing for prediction/forecasting, the value used for xt+1 is the predicted value for the next time period. It represents the forecast for the future based on the current and past data.
Exponential smoothing is a technique used to forecast time series data by assigning weights to previous observations. The weightage decreases exponentially as the observations go further back in time. The formula for exponential smoothing is:
xt+1 = α*xt + (1-α)*xt-1
Here, xt+1 is the forecast for the next period, xt is the value for the current period, xt-1 is the value for the previous period, and α is the smoothing constant (0 < α < 1) that determines the weight given to the current and past observations.