$\backslash$table$[[$Year$,1,2,3,4,5],[$Heart Transplants,$46\mathrm{.}0,50\mathrm{.}0,55\mathrm{.}0,54\mathrm{.}0,57\mathrm{.}0]]$

The director of medical services predicted $6$ years ago that demand in year $1$ would be $42\mathrm{.}0$ surgeries.

a$)$ Using exponential smoothing with $$ of $0\mathrm{.}60$ and the given forecast for year $1,$ the forecasts for years $2$ through $6$ are $($round your responses to one decimal place$)$:

$\backslash$table$[[$Year$,1,2,3,4,5,6],[$Forecast$,42\mathrm{.}0,44\mathrm{.}4,48\mathrm{.}0,52\mathrm{.}2,53\mathrm{.}3,55\mathrm{.}5]]$

For the forecast made using exponential smoothing with $=0\mathrm{.}60$ and the given forecast for year $1,$ MAD $=4\mathrm{.}42$ surgeries $($round your response to one decimal place$).$

Using exponential smoothing with $$ of $0\mathrm{.}90$ and the given forecast for year $1,$ the forecasts for years $2$ through $6$ are $($round your responses to one decimal place$)$:

$\backslash$table$[[$Year$,1,2,3,4,5,6],[$Forecast$,42\mathrm{.}0,45\mathrm{.}6,49\mathrm{.}6,54\mathrm{.}5,54\mathrm{.}0,56\mathrm{.}7]]$

For the forecast made using exponential smoothing with $=0\mathrm{.}90$ and the given forecast for year $1,$ MAD $=3\mathrm{.}46$ surgeries $($round your response to one decimal place$).$

b$)$ Forecasts for years $4$ through $6$ using a $3-$year moving average are $($round your responses to one decimal place$)$:

$\backslash$table$[[$Year$,4,5,6],[$Forecast$,50\mathrm{.}3,53,55\mathrm{.}3]]$

For forecasts made using a $3-$year moving average, MAD $=$ surgeries $($round your response to one decimal place$).$