## Exponential growth ends (with a whimper)

Here’s a second set of data on bacteria 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 (min) | No. of cells |
---|---|

0 | 4.3 × 10^{6} |

20 | 9.7 x 10^{6} |

40 | 22 x 10^{6} |

60 | 48 x 10^{6} |

80 | 97 x 10^{6} |

100 | 116 x 10^{6} |

120 | 118 x 10^{6} |

140 | 67 x 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?