# 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 * 10^{6} |

20 min | 9.7 * 10^{6} |

40 min | 22 * 10^{6} |

60 min | 48 * 10^{6} |

80 min | 97 * 10^{6} |

100 min | 116 * 10^{6} |

120 min | 118 * 10^{6} |

140 min | 67 * 10^{6} |

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. (Applet may take several seconds to load).

**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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