Question

Answer the question that was posed at the beginning of the lesson.

How can an absolute value equation describe the magnitude of an earthquake?

Include the following in your answer:

• a verbal and graphical explanation of how $\left|E-6.1\right|=0.3$describes the possible extremes in the variation of the earthquake’s magnitude, and
• an equation to describe the extremes for a different magnitude.

Short answer

Absolute value equation describes the uncertainty in the estimate of a magnitude of an earthquake. This means the equations gives a minimum and maximum estimate of an earthquake with a magnitude estimated on Richter scale.

On simplification of $\left|E-6.1\right|=0.3$for possible extremes in the variation of the earthquake’s magnitude we get maximum magnitude of earthquake is 6.4 and minimum magnitude of earthquake is 5.8

Now, let the magnitude on Richter scale be R and the actual magnitude for earthquake is E. As the uncertainty in the estimate of a magnitude of an earthquake is 0.3 so absolute value equation for extremes of a different magnitude is $\left|E-R\right|=0.3$

Step-by-step solution

- Answer “How can an absolute value equation describe the magnitude of an earthquake”

Absolute value equation describes the uncertainty in the estimate of a magnitude of an earthquake. This means the equations gives a minimum and maximum estimate of an earthquake with a magnitude estimated on Richter scale.

- Explain E-6.1=0.3

For any real number $a\text{and}b$with $b\ge 0$, if $\left|a\right|=b$then either a=b or a=-b

So given equation can be written as

$\begin{array}{c}E-6.1=0.3\text{or}x-6.1=-0.3\\ x=0.3+6.1\text{or}x=-0.3+6.1\\ x=6.4\text{or}x=5.8\end{array}$

So maximum magnitude of earthquake is 6.4 and minimum magnitude of earthquake is 5.8

- Equation with extremes for a different magnitude

Let the magnitude on Richter scale be R and the actual magnitude for earthquake is E. As the uncertainty in the estimate of a magnitude of an earthquake is 0.3 so absolute value equation for extremes of a different magnitude is $\left|E-R\right|=0.3$