Consider the following actual $($Upper A Subscript t$)$ and forecast $($Upper F Subscript t$)$ demand levels for a commercial multiline telephone at Office$$ Max:

$$

Time Period

t

Actual Demand

Upper A Subscript t

Forecast Demand

Upper F Subscript t

$1$

$45\mathrm{.}0$

$45\mathrm{.}00$

$2$

$48\mathrm{.}0$

$45\mathrm{.}00$

$3$

$60\mathrm{.}0$

$45\mathrm{.}90$

$4$

$47\mathrm{.}0$

$50\mathrm{.}13$

$5$

minus

$?$

The first$$ forecast, Upper F $1,$ was derived by observing Upper A $1$ and setting Upper F $1$ equal to Upper A $1.$ Subsequent forecasts were derived by exponential smoothing.