Look ahead at the scenario described in Prob. 27.7-3. Notice the steady trend upward in the number of applications over the past three years—from 4,600 to 5,300 to 6,000. Suppose now that the admissions office of Ivy College had been able to foresee this kind of trend and so had decided to use exponential smoothing with trend to do the forecasting. Suppose also that the initial estimates just over three years ago had been expected value = 3,900 and trend = 700. Then, with any values of the smoothing constants, the forecasts obtained by this forecasting method would have been exactly correct for all three years.
Illustrate this fact by doing the calculations to obtain these forecasts when the smoothing constant is α = 0.25 and the trend smoothing constant is β = 0.25. (Use hand calculations rather than an Excel template.)