Question $3($Fall $2021,$ Exam $1)$ The number of visitors to Grand Canyon is forecasted using Double Exponential Smoothing $($DES$),$ with intercept and slope at the end of January $($month $1)$ given as$,$ S$1=2,000$ and G$1=300.$

Assume that alpha $=0\mathrm{.}2$ and beta $=0\mathrm{.}1$ for all calculations.

$($a$)$ What is the one$-$step ahead forecast made in January for February?

FJan,Feb$=$

$($b$)$ What is the multi$-$step ahead forecast made in January for April?

FJan,April$=$