I am not quite sure how to use this information to express a function that would allow me to find the amount of energy released by the earthquake as asked in the question below.
The Richter magnitude scale is a scale of numbers used to tell the power (or magnitude) of earthquakes. Earthquakes $4.5$ or higher on the Richter scale can be measured all over the world. An earthquake size that scores $3.0$ is about $10$ times the amplitude of the one that scores $2.0$. The energy that is released increases by a factor of $32$. Every increase of $1$ on the Richter scale corresponds to an increase in energy released by a factor of $32$.
The Question: Describe the energy released by an earthquake using a function $E(m)$ of the Richter magnitude $m$. It also specifies that we need to make use of a constant $E_0$ for the amount of energy released by an earthquake with Richter magnitude $0.0$.
I have been able to find a function, however, I'm not quite sure it's the one that is required.
$$E(m) = 32(10^m) * E_0$$
Does that appear to be right?
Best Answer
I think you're looking for $E(m) = E_0 * 32^m$. As you have it written, the amount of energy released increases by a factor of 10 per unit of magnitude, and is 32 times the amount released at magnitude 0 at magnitude 0 ($E_0 = 32*E_0$), which is paradoxical. The amplitude stat seems to be a red herring, similar to the point about a 4.5 magnitude earthquake being measurable around the world.