The Richter Scale is a commonly used way to measure the size of an earthquake.

It measures the amplitude (size) of the seismic waves generated by the earthquake using a logarithmic scale, which means that the number that an earthquake registers on the Richter Scale gives the exponent of 10 of the amplitude. So if an earthquake registers a 3.4 on the Richter scale, the amplitude of the seismic wave is (roughly) 10_{3.4.} In 2011, there was an earthquake centered near Mineral, Virginia, that registered a 5.8 on the Richter scale; this was the largest recorded earthquake on the East Coast of the United States. On March 5th of this year, there was an earthquake centered near Hartford, Connecticut, that registered a 1.9 on the Richter Scale. How many times more powerful was the 2011 earthquake than the recent earthquake?

I said this,

2011= 5.8

2021= 1.9

The 2011 earthquake was 3.06 stronger than the 2009 earthquake.

But I don't know if I did it right or if there is more I need to do, I think that there is but I just don't know what to do. Could you also explain how you got what you got? thanks so much.

liz54321 Mar 31, 2021

#1**+1 **

Its a little unclear to me what it means by "powerful" so I can understand how this question is a bit confusing.... maybe there is a specific meaning of the word "powerful" here and I just don't know it! But because of the fact that it bothers to tell us that the number on the Richter Scale is the exponent of 10 of the amplitude..... I'm guessing that perhaps the actual question it's asking is this:

How many times greater was the amplitude of the 2011 earthquake than the amplitude of the 2021 earthquake?

amplitude of the 2011 earthquake = 10^{5.8}

amplitude of the 2021 earthquake = 10^{1.9}

Now the question is: 10^{5.8} is how many times greater is than 10^{1.9} ?

Or in other words... 10^{5.8} is equal to *what* times 10^{1.9} ?

\(10^{5.8}\ =\ x\cdot10^{1.9}\)

Divide both sides of the equation by 10^{1.9} to solve for x

\(\dfrac{10^{5.8}}{10^{1.9}}\ =\ x\)

Now we can apply the rule which says \(\frac{x^a}{x^b}\ =\ x^{a-b}\)

\(10^{5.8-1.9}\ =\ x \\~\\ 10^{3.9}\ =\ x\)

And so the amplitude of the 2011 earthquake is 10^{3.9} times greater than the amplitude of the 2021 earthquake.

However, I could be misinterpreting this question too, and your original answer might be correct! Just because they told us that information about the Richter scale doesn't necessarily mean we have to use it to answer the question....maybe they were just trying to throw us off with a red herring

hectictar Mar 31, 2021