The following table provides information on surgeries at a local hospital. The data shows that surgeries have been

steadily increasing over the past few years.

Year $123456$

Heart Transplants $4550525658?$

$2\mathrm{.}1.$ Use exponential smoothing, first with a smoothing constant of $0\mathrm{.}6$ and then one with smoothing constant of $0\mathrm{.}9$

to develop forecasts for years $2$ to $6.(6$ marks$)$

$2\mathrm{.}2.$ Use a $3-$year moving average to forecast demand in years $4,5$ and $6.(4$ marks$)$

$2\mathrm{.}3.$ Use the trend projection method to forecast demand in year $6.(10$ marks$)$