Why It Matters: Growth Models
The following essay is adapted from blog posts on emergent math by Geoff Krall.
Can You Predict How Many Followers @charliesheen Has Right Now?
Sometime on March 1, 2011, Charlie Sheen joined twitter at the suggestion of Piers Morgan, who is apparently some type of person. By the time I was alerted of the existence of a @charliesheen twitter feed, it was 4:04 PM Mountain Standard Time. Sheen had yet to tweet, but already had somehow amassed over 100,000 followers. He hadn’t even put up an avatar of himself yet (and somehow the account was “verified”).
Time on March 1, 2011 | # of Followers |
---|---|
4:04 PM | 109,099 |
4:07 PM | 112,497 |
4:09 PM | 116,143 |
4:12 PM | 120,195 |
4:14 PM | 122,901 |
4:18 PM | 127,643 |
4:21 PM | 129,793 |
4:24 PM | 133,357 |
4:29 PM | 140,215 |
4:32 PM | 144,103 |
4:38 PM | 149,528 |
4:44 PM | 153,848 |

Time on March 1, 2011 | # of Followers |
---|---|
6:21 PM | 261,894 |
6:24 PM | 275,638 |
6:49 PM | 302,077 |
7:13 PM | 324,595 |
7:38 PM | 348,955 |
8:45 PM | 429,904 |
Time on March 2, 2011 | # of Followers |
---|---|
6:45 AM | 729,703 |
8:51 AM | 799,008 |
9:36 AM | 820,538 |
10:23 AM | 841,940 |
11:16 AM | 865,972 |
12:43 PM | 902,291 |
1:47 PM | 926,557 |
3:09 PM | 957,259 |
- At what time March, 1, did Charlie Sheen join twitter? and,
- How many followers does he have right now?






Learning Objectives
Linear and Geometric Growth- Build a recursive equation that models linear or exponential growth
- Build an explicit equation that models linear or exponential growth
- Make predictions using linear and exponential growth models
- Use logarithms to solve exponential growth models for time
- Identify the carrying capacity and growth rate of the logistic growth model
- Use the logistic growth model to make predictions