The president of State University wants to forecast student enrollments for this academic year based on the following historical data: Year Enrollments 5 Years ago 15,000 4 Years ago 16,000 3 Years ago 18,000 2 Years ago 20,000 Last Year 21,000 What is the forecast for this year using trend-adjusted (double) smoothing with alpha

19,500

Explanation:

Calculation for the Forecast for this year

First step is to calculate the Forecast for last year

Forecast for last year= [(1 - 0.5 ) × 16,000 ) + ( 0.5 × 20,000)]

Forecast for last year= [(0.5 × 16,000 ) + ( 0.5 × 20,000)]

Forecast for last year= 8,000 + 10,000

Forecast for last year= 18,000

Now let calculate the Forecast for this year

Forecast for this year= [(1 - 0.5 ) × 18, 000 ) + ( 0.5 × 21,000)]

Forecast for this year= [(0.5 × 18, 000 ) + ( 0.5 × 21,000)]

Forecast for this year= 9,000 + 10,500

Forecast for this year= 19,500

Therefore the Forecast for this year will be 19,500