The sequence for the given situation is:
[tex]\begin{gathered} y_0=1 \\ \\ y_x=1+2(y_{x-1}) \end{gathered}[/tex]
y (number of people who know about the soft opening
y0: number of people who know about the soft opening at day 0
As each person will tell 2 people about the soft opening you multiply the number of people of previous dat (y(x-1)) by 2 and add to it the initial number of people (1).
Then, the data in the table is find using the formula of the sequence above:
[tex]\begin{gathered} y_2=1+2(y_1) \\ y_2=1+2(3) \\ y_2=1+6 \\ y_2=7 \\ \\ \\ y_3=1+2(y_2) \\ y_3=1+2(7) \\ y_3=1+14 \\ y_3=15 \\ \\ \\ y_4=1+2(y_3) \\ y_4=1+2(15) \\ y_4=1+30 \\ y_4=31 \\ \\ \\ y_5=1+2(y_4) \\ y_5=1+2(31) \\ y_5=1+62 \\ y_5=63 \end{gathered}[/tex]
You get the next table:
