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

Down and dirty with e-to-the-t

Here is the equation we have so far:

N_t = N₀ * 2^ts

what we need to do is get rid of the "ts" and put in a t.

We've already been using the relationship :

# timesteps = actual time / generation length

So, for E nice, if the actual time is 50 minutes and the generation length is 20 minutes, then

# timesteps = 50/20 = 2.5

Likewise for E. quick:

#timesteps = 50/15 = 3.33

We can get rid of "ts" in the above equation by substituting actual time / generation length, or in other words

t/g

Now our equation looks like this:

N_t = N₀ * 2^t/g

This change looks very small, but it's actually quite important. It is simpler to find population size as a function of t, and much more importantly, now we can compare the population sizes by graphing them against actual time.