After plotting demand for four periods, an emergency room manager has concluded that a trend$-$adjusted exponential smoothing model

is appropriate to predict future demand. The initial estimate of trend is based on the net change of $30$ for the three periods from $1$ to $4,$

for an average of $+10$ units. Use $=\mathrm{.}5$ and $=\mathrm{.}4,$ and TAF of $250$ for period $5.$ Obtain forecasts for periods $6$ through $10.$Using the combination of trend and seasonality, what is the forecast demand of January of next year?