The strength of an earthquake is measured on a logarithmic scale called the Richter scale. The amplitude, $A$, of the seismic waves of an earthquake is compared to $A_0$, the amplitude of the seismic waves of a chosen standard earthquake. The Richter scale rating, $M$, of an earthquake with seismic wave amplitude $A$ is given by $$M=\log\left(\frac{A}{A_0}\right).$$

a) In January 2011, Seattle Seahawks fans started an earthquake with a rating of 1 on the Richter scale, cheering on running back Marshawn Lynch during a 67-yard touchdown run. How many times larger were the seismic waves of the so-called "Beast Quake" than than those of the standard earthquake?

b) In April 2015, seismographs measured the Nepal earthquake to have a Richter scale rating of 7.8. How many times larger were the seismic waves of the Nepal earthquake than those of the standard earthquake?

c) Aftershocks of the Nepal earthquake rated as high as 7.3 on the Richter scale. How many times larger were the seismic waves of the strongest aftershocks than those of the standard earthquake?

Hint: