Use the Data Given Below to Answer the Following Question(s)

Multiple Choice

Use the data given below to answer the following question(s) .
The table provided below gives the sales details of the number of android smart phones at an electronic retail store for the past 6 weeks.The time series appears to be relatively stable, without trend, seasonal, or cyclical effects.The value of k is set at 3.(Hint: Optimize α value.)
$\begin{array}{|c|c|}\hline \text { Week } & \text { Units sold } \\\hline 1 & 88 \\\hline 2 & 44 \\\hline 3 & 54 \\\hline 4 & 65 \\\hline 5 & 72 \\\hline 6 & 85 \\\hline\end{array}$
-What is the formula used to calculate the value of at in the linear trend equation Ft₊k = at + btk while using double exponential smoothing?

A) a_t = β(b_t - bt₋₁) + (1 -β) bt₋₁
B) a_t = αF_t₋₁ + (1 - α) (a_{t ₊₁} + b_t₊₁)
C) a_t = αF_t + (1 - α) (a_{t ₋₁} + b_t₋₁)
D) a_t = β(b_t + b_t₋₁) + (1 + γ) b_t₋₁