Extended problem:
Exponential growth ends (with a whimper)
Here's a second set of data on meningococcal growth rates. Your instructions are
1) to determine the exponential growth rate of the bacteria, and
2) to determine when growth stops being exponential.
| time | popn |
|---|---|
| 0 min | 4.3 * 106 |
| 20 min | 9.7 * 106 |
| 40 min | 22 * 106 |
| 60 min | 48 * 106 |
| 80 min | 97 * 106 |
| 100 min | 116 * 106 |
| 120 min | 118 * 106 |
| 140 min | 67 * 106 |
Just look at the data first... what can you see with your bare eyes, so to speak?
About doubling time:
About the general shape of the population trajectory:
About when growth begins to slow down:
Now try plotting the data.
Which time period showed exponential growth:
Let's look at an untransformed graph to figure out the doubling time. We could do this on the log-transformed graph above, but its difficult because the y-axis is on a log scale.
Where should we start, and what is the growth rate?
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