As you may remember, earthquake magnitudes are measured by the amount of energy that is released. Since the amount of energy released from a large earthquake can be millions of times greater than the energy released by a small quake, a scale was created (the Richter scale) to give magnitudes in numbers that are easy to use. An earthquake measuring $3.4$ on the Richter scale, for example, releases $10^{3.4}$ kilojoules of energy.

1. How many times more energy is released by an earthquake that measures $6.5$ on the Richter scale than an earthquake that measures $5.5$?

   Hint (a):

   Solve the equation:
   $x · 10^{5.5} = 10^{6.5}$

   Answer (a): 

   10 times more energy.

2. How many times more energy is released by an earthquake that measures $5.1$ than an earthquake that measures $4.3$? Give your answer both as a power of $10$ and as a decimal.

   Answer (b):

   $10^{0.8} = 6.310$

3. What would the magnitude be of an earthquake that released half as much energy as an earthquake measuring 6.2 on the Richter scale?

   Answer (c):

   $5.9$