Scenario A: At noon, you get some great news but you need to keep it a secret. I

Question

Scenario A: At noon, you get some great news but you need to keep it a secret. It’s just too good to keep to yourself; so 5 minutes after you get the news you call 2 friends and tell them, but swear them to secrecy. They understand how important it is to keep a secret, so they don’t tell anybody. After 5 more minutes you call 2 more friends, and again they keep your secret. You are just so excited that after 5 more minutes you make your third set of calls and tell two more friends. Fill in the table below to show how many people are told and how many people know the secret after each 5 minute interval. Time 5 minute interval = n Number of people told Number of people who know 12:00 0 1 12:05 1 2 12:10 2 12:15 3 12:20 4 12:25 5 12:30 6 12:35 7 12:40 8 12:45 9 12:50 10 12:55 11 1:00 12 Scenario B: Suppose you call the first two friends at 12:05 and you are satisfied because you’ve shared your secret, so you don’t 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. Fill in the table below to show how many people are told and how many people know the secret after each 5 minute interval. Time 5 minute interval = n Number of people told Number of people who know 12:00 0 1 12:05 1 2 12:10 2 12:15 3 12:20 4 12:25 5 12:30 6 12:35 7 12:40 8 12:45 9 12:50 10 12:55 11 1:00 12 How many people know your secret at 12:40 in Scenario A? In Scenario B? Describe the pattern of growth in the “Number of people told” column for both Scenario A and Scenario B. Describe the pattern of growth in the “Number of people who know” column for both Scenario A and Scenario B. Write an equation to find the “Number of people told” for any 5-minute interval(n) in Scenario A. Write an equation to find the “Number of people told” for any 5-minute interval in Scenario B. Write an equation to find the “Number of people who know” for any 5-minute interval in Scenario A. Write an equation to find the “Number of people who know” for any 5-minute interval in Scenario B.

Explanation / Answer

Scenario A Time No of interval Number of people told Number of people who know (5 minute interval) 12.00 0 0 1 12.05 1 2 3 12.10 2 4 5 12.15 3 6 7 12.20 4 8 9 12.25 5 10 11 12.30 6 12 13 12.35 7 14 15 12.40 8 16 17 12.45 9 18 19 12.50 10 20 21 12.55 11 22 23 1.00 12 24 25 a) How many people know your secret at 12:40 in Scenario A = 17 b) Describe the pattern of growth in the “Number of people told” column for Scenario A = Constant pattern of Growth c) Describe the pattern of growth in the “Number of people who know” column for Scenario A = Constant pattern of Growth d) Write an equation to find the “Number of people told” for any 5-minute interval(n) in Scenario A = No of interval x 2 e) Write an equation to find the “Number of people who know” for any 5-minute interval in Scenario A = No of interval x 2 +1 Scenario B Time No of interval Number of people told Number of people who know (5 minute interval) 12.00 0 0 1 12.05 1 2 3 12.10 2 6 7 12.15 3 14 15 12.20 4 30 31 12.25 5 62 63 12.30 6 126 127 12.35 7 254 255 12.40 8 510 511 12.45 9 1022 1023 12.50 10 2046 2047 12.55 11 4094 4095 1.00 12 8190 8191 a) How many people know your secret at 12:40 in Scenario B = 511 b) Describe the pattern of growth in the “Number of people told” column for Scenario B = Incremental pattern of growth c) Describe the pattern of growth in the “Number of people who know” column for Scenario B = Incremental pattern of growth d) Write an equation to find the “Number of people told” for any 5-minute interval(n) in Scenario B = {(2)^ (No of interval + 1)} -2 e) Write an equation to find the “Number of people who know” for any 5-minute interval in Scenario B = [{(2)^ (No of interval + 1)} -2]+1

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