The president of State University wants to forecast student enrollment 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 exponential smoothing with trend if $\backslash$alpha $=0\mathrm{.}5$ and $\backslash$beta $=0\mathrm{.}3?$ Assume the forecast for last year was $20,000$ and the forecast for two years ago was $19,000,$ and that the trend estimate for last year's forecast was $2,000.$