Table of Contents

• Section 1. How the Vibrio population grows
• 1: What causes cholera?
• 2: Build the basic growth equation
• 3: Draw exponential growth
• Section 2. So why isn't Matt dead already?
• 4: How long until 1 million bacteria?
• 5: All we need now is data
• 6: Looking at data
• 7: Log transform straightens out exponential growth
• 8: Do ALL curves get "straightened" by taking the log?
• 9: Phases of bacterial growth
• Section 3. How can we tell when the population is growing exponentially?
• 10: A test for exponential growth
• 11: And the answer is...
• 12: To recap
• 13: Some more practice
• 14: Extended problem: Exponential growth ends
• Review
• 15: Summary

Review

The infective dose (ID) for cholera is about 1 million. It would take about 20 generations of doubling for a population starting from a single cell to reach 1 million cells.

Exponential growth follows the pattern

• Initial Number --> 1
• Number after 1 doubling --> 1×2
• Number after 2 doublings --> 1×2×2
• Number after 3 doublings --> 1×2×2×2

The (untransformed) graph is a line curved up. When the graph is log-transformed, it becomes a straight line (pointing up, assuming the population is growing). This happens because during exponential growth, the population always grows by the same multiplicative factor.

Using knowledge about how the log-transformed graph appears, we can determine whether a bacterial population is in a lag, log, stability, or death phase.

We can determine doubling time roughly by reading it off a graph. To do this, pick a starting population (on the y axis) which falls within the exponential growth window. Find the doubled population and check that it also falls within the exponential growth window. Find the amount of time elapsed (on the x axis) between the two population readings. This is the approximate doubling time.

Another way to estimate doubling time would be to calculate it based on data about how long it takes to get to the infective dose, and how many generations that represents.