Question 1189653
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Part A


Plug in M = 9.0 into the formula given


E(M) = (10^1.5)^M
E(9) = (10^1.5)^9
E(9) = (31.6227766016838)^9
E(9) = 31,622,776,601,683.9
E(9) = 32,000,000,000,000
E(9) = <font color=red>3.2 * 10^13</font>
Roughly 32 trillion kWh of energy was released.


Answer: <font color=red>3.2 * 10^13 kWh</font>


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Part B


This time we'll plug in M = 6.9


E(M) = (10^1.5)^M
E(6.9) = (10^1.5)^6.9
E(6.9) = (31.6227766016838)^6.9
E(6.9) = 22,387,211,385.6834
E(6.9) = 22,000,000,000
E(6.9) = <font color=red>2.2 * 10^10</font>
Roughly 22 billion kWh of energy was released.


Answer: <font color=red>2.2 * 10^10 kWh</font>


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Part C


Divide the results of parts A and B
A/B = (3.2 * 10^13)/(2.2 * 10^10)
A/B = 1,454.54545454546
A/B = <font color=red>1455</font>


Answer: <font color=red>Roughly 1455 times greater</font>


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Part D


Unlike parts A and B, we don't know what M is. 
But we do know that E(M) = 3,981,000 kWh. 
We'll plug this in to find M. 
You'll need to use logarithms.


E(M) = (10^1.5)^M
3,981,000 = (10^1.5)^M
3,981,000 = (31.6227766016838)^M
log(3,981,000) = log( (31.6227766016838)^M )
log(3,981,000) = M*log( 31.6227766016838 )
M = log(3,981,000)/log( 31.6227766016838 )
M = 4.39999478505607
M = <font color=red>4.4</font>
The magnitude on the Richter Scale is roughly a <font color=red>4.4</font>


If you were to plug M = 4.4 into the formula given, then,
E(M) = (10^1.5)^M
E(M) = (31.6227766016838)^M
E(4.4) = (31.6227766016838)^4.4
E(4.4) = 3,981,071.70553498
E(4.4) = 3,981,072
which isn't too far off the mark of the figure 3,981,000


Answer: <font color=red>Magnitude 4.4</font>
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