Question

suppose you call the first two friends at 12:05 and you are satisfied because youve shared your secret, so you dont tell anybody else. unfortunately, none of your friends can keep a secret. like you, they just need to tell two friends, but then each of those friends needs to tell two friends, and so on, and so on.

fill in the table below to show how many people are told and how many people know the secret after each 5 minute interval.

\

$$\begin{tabular}{|c|c|c|c|} \\hline time & \\begin{tabular}{c} 5 \\\\ minute \\\\ interval \\\\ (n) \\end{tabular}$$

& \

$$\begin{tabular}{c} number of \\\\ people told \\end{tabular}$$

& \

$$\begin{tabular}{c} number of \\\\ people who know \\end{tabular}$$

\\\\
\hline
12:00 & 0 & - & 1 \\\\
\hline
12:05 & 1 & 2 & 3 \\\\
\hline
12:10 & 2 & 4 & 7 \\\\
\hline
12:15 & 3 & 8 & 15 \\\\
\hline
12:20 & 4 & & \\\\
\hline
12:25 & 5 & & \\\\
\hline
12:30 & 6 & & \\\\
\hline
12:35 & 7 & & \\\\
\hline
12:40 & 8 & & \\\\
\hline
12:45 & 9 & & \\\\
\hline
12:50 & 10 & & \\\\
\hline
12:55 & 11 & & \\\\
\hline
1:00 & 12 & & \\\\
\hline
\end{tabular}

Explanation:

Identify the pattern for the number of people told

$$
LATEXBLOCK0
$$

Identify the pattern for the total number of people who know

$$
LATEXBLOCK1
$$

Calculate the values for intervals 4 through 12

$$
LATEXBLOCK2
$$

Answer:

Time	5 minute interval (\(n\))	Number of people told	Number of people who know
12:05	1	2	3
12:10	2	4	7
12:15	3	8	15
12:20	4	16	31
12:25	5	32	63
12:30	6	64	127
12:35	7	128	255
12:40	8	256	511
12:45	9	512	1023
12:50	10	1024	2047
12:55	11	2048	4095
1:00	12	4096	8191