# Homework Help: Timescales physics problem

1. Jan 27, 2005

Hello all

Let $$\delta t$$ be a timestep. Then the mean is equaled to $$\mu\delta t$$ where $$\mu$$ is a constant. Assuming a nornal distribution, $$\frac{S_{i+1}-S_{i}}{S_i} = \mu\delta t$$

$$S_{i+1} = S_i(1 + \mu\delta t)$$. Hence after M timesteps we have:

$$S_m = S_0(1+\mu\delta t)^M = S_0e^{Mlog(1+\mu\delta t)} \doteq S_{M}=S_{0}e^{[\mu M(\delta t)]}= S_0e^{\mu T}$$ How do we get the last part (the approximation)?

Thanks

Last edited: Jan 27, 2005
2. Jan 27, 2005

### dextercioby

The way i see it,the approximation should be
$$S_{M}=S_{0}e^{[\mu M(\delta t)]}$$

It might help if you came up with more explanation.

Daniel.

3. Jan 27, 2005

yes that is correct. how do they get this? do they use taylor series?

4. Jan 27, 2005

### dextercioby

No,the definition of "e"...Check one of the other threads where i showed you on a similar problem...

Daniel.