Question: \(\mathrm{ABC}\), Inc. has estimated the following simple regression model of sales using weekly sales figures representing the firm's sales history over the past few years:

\[\begin{array}{rlr}

\operatorname{lnS}_{t}= & 14.221+.052 \mathrm{t} & \mathrm{R}^{2}=.99 \\

& (.03) & (.02) &

\end{array}\]

where \(S_{t}\) is unit sales in time period (week) \(t\) and the numbers in parentheses are the standard deviations of the two regression coefficients.

1. Express this sales forecasting model in the form of the constant rate of change growth model with continuous compounding:
   \[\mathrm{S}_{\mathrm{t}}=\mathrm{S}_{0} \mathrm{e}^{\mathrm{gt}}\]
   i.e., determine the values for \(S_{0}\) and \(g\) in this case of continuous compounding.
2. Forecast the value of \(\mathrm{t}\) at which sales will equal $2,500,000 units.

Price: $2.99

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