Table of Contents

• Pre-quiz
• Part I: Exponential Growth
• 1: Building the basic growth equation
• 2: What does exponential growth look like?
• 3: Why does the semi-log plot unbend the plot of exponential growth?
• 4: Do ALL curves get 'unbent' by taking the log?
• Part II: Finding Generation Time
• 5: But how long is a generation?
• 6: Finding generation time on a graph
• 7: Is this growth exponential?
• Part III: The Numbers get messy
• 8: In search of ... the exact doubling time
• 9: Finding doubling time with messy numbers
• 10: Doubling time practice for fun and profit
• 11: In Search of ... a more convenient equation
• 12: Down and dirty with e-to-the-t
• 13: Comparing apples and oranges
• Part IV: Extended Problems
• 14: Fun with Rhizobia
• 15: Extended problem #1: E. coli ate my lab report
• 16: Extended problem #2: Exponential growth ends (with a whimper)
• 17: More practice with exponential growth

Finding doubling time with messy numbers

Recall that we started out with an equation:

N_t = N₀ 2^g

Let's say I told you that N₀ was 10 million and N_t was 80 million one hour later. You would probably think to yourself, "well, the population doubled three times, from 10 to 20 million, from 20 to 40 million, and from 40 to 80 million. Since three doublings took 1 hour, that means each doubling took 20 minutes."

Another somewhat fancier way of getting the same answer would be to substitute the information that you know (N_t and N₀) into the equation above, and solve for the information that you don't know (number of generations, g). Here's how that would look:

 

 

We will need to do same basic procedure with messier numbers. Let's say the population increased from 10 to 70 million in one hour.

 

In a word: when you have a problem with exponents, try logs. By now you should have seen logs in several of these modules, but if you don't remember the basics, you can visit the logs and pH module for a refresher. Remember, logs are a biologist's best friend.