With a smoothing constant of $=0\mathrm{.}4,$ the exponential smoothing forecast equation

$$t $+1=$Yt $+(1)$t

shows that the forecast for week $13$ of the gasoline sales data from the table is given by

$13=0\mathrm{.}4$Y$12+0\mathrm{.}612.$

However, the forecast for week $12$ is given by

$12=0\mathrm{.}4$Y$11+0\mathrm{.}611.$

Thus, we could combine these two results to show that the forecast for week $13$ can be written

$13=0\mathrm{.}4$Y$12+0\mathrm{.}6(0\mathrm{.}4$Y$11+0\mathrm{.}611)=0\mathrm{.}4$Y$12+0\mathrm{.}24$Y$11+0\mathrm{.}3611.$