00:01
Let's discuss a few applications of some general concepts regarding exponential functions.
00:08
So we want to know the limitations to an exponential function with growth models.
00:12
So for example, let's say we have a bacterial culture that's doubling every hour.
00:18
So we know that eventually the bacterial culture is going to take up its space and it'll run out of nutrients, in which case this is going to level off.
00:26
So an exponential model is only good at looking at snapshots in time, but it does not.
00:30
Hold true as x goes to infinity necessarily.
00:34
Oftentimes it won't.
00:36
Then if we look at why 5 % per year compounded continuously yields more than 5 % compounded monthly is because that's the difference between the a equals p e to the r t versus our other model where it's going to be every month it's compounded.
00:55
We see that this is going to be continuous at a continuous rate so it's going to be growing faster.
01:03
Then we want to, we can consider some graphs to determine some data.
01:12
We can also predict based on data and charts we're given...