$"$As you can see in the following$$ table, demand for heart transplant surgery at Washington General Hospital has increased steadily in the past few$$ years:

$$

Year

$1$

$2$

$3$

$4$

$5$

Heart Transplants

$45\mathrm{.}045\mathrm{.}0$

$48\mathrm{.}048\mathrm{.}0$

$53\mathrm{.}053\mathrm{.}0$

$57\mathrm{.}057\mathrm{.}0$

$57\mathrm{.}057\mathrm{.}0$

The director of medical services predicted $6$ years ago that demand in year $1$ would be $41\mathrm{.}041\mathrm{.}0$ surgeries.$$

Part $2$

$$a$)$ Using exponential smoothing with alpha$\backslash$alpha of $0\mathrm{.}600\mathrm{.}60$ and the given forecast for year$1,$ the forecasts for years $2$ through $6$ are $($round your responses to one decimal $$place$)$:

Year

$1$

$2$

$3$

$4$

$5$

$6$

Forecast

$41\mathrm{.}041\mathrm{.}0$

$43\mathrm{.}443\mathrm{.}4$

$46\mathrm{.}246\mathrm{.}2$

$50\mathrm{.}350\mathrm{.}3$

$54\mathrm{.}354\mathrm{.}3$

$55\mathrm{.}955\mathrm{.}9$

Part $3$

For the forecast made using exponential smoothing with alpha$\backslash$alpha $=0\mathrm{.}600\mathrm{.}60$ and the given forecast for year$1,$ MAD$=5\mathrm{.}05\mathrm{.}0$ surgeries $($round your response to one decimal place$).$

Part $4$

Using exponential smoothing with alpha$\backslash$alpha of $0\mathrm{.}900\mathrm{.}90$ and the given forecast for year$1,$ the forecasts for years $2$ through $6$ are $($round your responses to one decimal $$place$)$:

Year

$1$

$2$

$3$

$4$

$5$

$6$

Forecast

$41\mathrm{.}041\mathrm{.}0$

$44\mathrm{.}644\mathrm{.}6$

$47\mathrm{.}747\mathrm{.}7$

$52\mathrm{.}552\mathrm{.}5$

$56\mathrm{.}656\mathrm{.}6$

$57\mathrm{.}057\mathrm{.}0$

Part $5$

For the forecast made using exponential smoothing with alpha$\backslash$alpha $=0\mathrm{.}900\mathrm{.}90$ and the given forecast for year$1,$ MAD$=3\mathrm{.}53\mathrm{.}5$ surgeries $($round your response to one decimal place$).$

Part $6$

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

Year

$4$

$5$

$6$

Forecast

$48\mathrm{.}748\mathrm{.}7$

$52\mathrm{.}752\mathrm{.}7$

$55\mathrm{.}755\mathrm{.}7$

Part $7$

For forecasts made using a$3-$year moving$$ average, MAD$=6\mathrm{.}36\mathrm{.}3$ surgeries $($round your response to one decimal place$).$

Part $8$

$$c$)$ Forecasts for years $1$ through $6$ using the$$ trend$-$projection method are $($round your responses to one decimal $$place$)$:

Year

$1$

$2$

$3$

$4$

$5$

$6$

Forecast

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