The energy (in joules) released by an earthquake of magnitude M is given by the equation E = 25,000 • 10^1.5M. (This equation can be solved for M to define the magnitude of a given earthquake; it is a refinement of the original Richter scale created by Charles Richter in 1935.)

a. Compute the energy released by earthquakes of magnitude 1, 2, 3, 4, and 5. Plot the points on a graph and join them with a smooth curve.

b. Compute dE/dM and evaluate it for M = 3. What does this derivative mean? (M has no units, so the units of the derivative are J per change in magnitude.)