Electromagnetic shower energy spectrum

[vbrasic]

Homework Statement

The energy of a daughter particle in electromagnetic shower is approximated by, $E(t)=\frac{E_0}{2^t}$. Show that the energy falls off like approximately $E^{-2}$, for small $E$.

Homework Equations

Nothing really. Just a matter of knowing how to differentiate.

The Attempt at a Solution

I have that the rate of change of the energy is given by $\frac{dE}{dt}=-\frac{\ln(2)E_0}{2^t}$. However, I'm not sure how to approximate this by $-E^{-2}=-\frac{2^{2t}}{E_0^2}$, which is what I think I'm supposed to be doing.

 

[mfb]

How can the energy fall off with increasing energy? Is that really the precise problem statement?

However, I'm not sure how to approximate this by $-E^{-2}=-\frac{2^{2t}}{E_0^2}$.

That is just the initial equation squared, inverted and with a minus sign on both sides. I don't think that is the goal.