# Down and dirty with e-to-the-t

Here is the equation we have so far:

N_{t} = N_{0} * 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} = N_{0} * 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.

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