Question

2. Let x represent the day number and let y be the number of people who know about the soft opening on day x. Consider the day before Jan told anyone to be Day 0, so that Jan is the only person who knows about the opening on Day 0. Day 1 is the first day that Jan told two people about the opening. a. Complete the following table. Day0 1 2 3 4 5 Number of people who know 1 3

Answer 1

The sequence for the given situation is:

`\begin{gathered} y_0=1 \\ \\ y_x=1+2(y_(x-1)) \end{gathered}`

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:

`\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}`

You get the next table: