$1.$ The Bonavista patient transfer company is considering the purchase of a new ambulance. The decision will rest partly on the anticipated mileage to be driven next year. The kilometers driven during the past $5$ years are as follows:

Year Distance $($KM$)$

$13,000$

$24,000$

$33,400$

$43,800$

$53,700$

d$.$ Compute the forecast for year $6$ using exponential smoothing, an initial forecast for year $1$ of $3,000$ miles, and a $=\mathrm{.}5$