interval. ive completed the first several rows for you.

\begin{tabular}{|c|c|c|c|}
\hline
time & 5 minute interval (n) & number of people told & number of people who know \\
\hline
12:00 & 0 & - & 1 \\
\hline
12:05 & 1 & 2 & 3 \\
\hline
12:10 & 2 & 2 & 5 \\
\hline
12:15 & 3 & & \\
\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
\end{tabular}

Question

interval. ive completed the first several rows for you.

\begin{tabular}{|c|c|c|c|}
\hline
time & 5 minute interval (n) & number of people told & number of people who know \\
\hline
12:00 & 0 & - & 1 \\
\hline
12:05 & 1 & 2 & 3 \\
\hline
12:10 & 2 & 2 & 5 \\
\hline
12:15 & 3 & & \\
\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
\end{tabular}

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Geometric Sequences", "Arithmetic Sequences" ], "new_concepts": [ "Rumor Spread Modeling" ], "current_concepts": [ "Geometric Sequences", "Arithmetic Sequences", "Rumor Spread Modeling" ] } ## Identify the pattern of rumor propagation $$ \begin{aligned} &n = 0: \text{Number of people told} = -, \text{Total who know} = 1 \ &n = 1: \text{Number of people told} = 2, \text{Total who know} = 1 + 2 = 3 \ &n = 2: \text{Number of people told} = 2, \text{Total who know} = 3 + 2 = 5 \ &\text{Since the number of people told in each 5-minute interval is constant at } 2: \ &\text{Number of people told } (n \ge 1) = 2 \ &\text{Total who know } (n) = 2n + 1 \end{aligned} $$ ## Calculate values for each interval $$ \begin{aligned} &n = 3: \text{Told} = 2, \text{Total} = 2(3) + 1 = 7 \ &n = 4: \text{Told} = 2, \text{Total} = 2(4) + 1 = 9 \ &n = 5: \text{Told} = 2, \text{Total} = 2(5) + 1 = 11 \ &n = 6: \text{Told} = 2, \text{Total} = 2(6) + 1 = 13 \ &n = 7: \text{Told} = 2, \text{Total} = 2(7) + 1 = 15 \ &n = 8: \text{Told} = 2, \text{Total} = 2(8) + 1 = 17 \ &n = 9: \text{Told} = 2, \text{Total} = 2(9) + 1 = 19 \ &n = 10: \text{Told} = 2, \text{Total} = 2(10) + 1 = 21 \end{aligned} $$ | Time | 5 minute interval ($n$) | Number of people told | Number of people who know | |---|---|---|---| | 12:00 | 0 | — | 1 | | 12:05 | 1 | 2 | 3 | | 12:10 | 2 | 2 | 5 | | 12:15 | 3 | 2 | 7 | | 12:20 | 4 | 2 | 9 | | 12:25 | 5 | 2 | 11 | | 12:30 | 6 | 2 | 13 | | 12:35 | 7 | 2 | 15 | | 12:40 | 8 | 2 | 17 | | 12:45 | 9 | 2 | 19 | | 12:50 | 10 | 2 | 21 | { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Arithmetic Sequences" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the pattern of rumor propagation

Calculate values for each interval

Answer:

Time	5 minute interval (\(n\))	Number of people told	Number of people who know
12:05	1	2	3
12:10	2	2	5
12:15	3	2	7
12:20	4	2	9
12:25	5	2	11
12:30	6	2	13
12:35	7	2	15
12:40	8	2	17
12:45	9	2	19
12:50	10	2	21