MathBench > Population Dynamics

Bacterial Growth:
The E. coli ate my homework

Down and dirty with e-to-the-t

Here is the equation we have so far:

Nt = N0 * 2ts

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


Now our equation looks like this:

Nt = N0 * 2t/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.