Question

Compare the intensities of the two earthquakes. (Round to the nearest whole number.)

Answer 1

Step 1

Given;

`\begin{gathered} First\text{ earthquake\lparen M}_a)\text{ =7.9} \\ second\text{ earthquake\lparen M}_b)\text{=4.1} \end{gathered}`

Step 2

State the magnitude and intensity formula we can use to solve this problem

`\begin{gathered} M_a=log((I_a)/(I_o)_)) \\ M_b=log((I_b)/(I_o)) \end{gathered}`
`\begin{gathered} 10^(7.9)=(I_a)/(I_o) \\ 10^(4.1)=(I_b)/(I_o) \\ \end{gathered}`
`Solve\text{ for I}_a\text{ and I}_b`
`\begin{gathered} 10^(7.9)(I_o)=I_a \\ 10^(4.1)(I_o)=I_b \\ (I_a)/(I_b)=(10^(7.9)(I_o))/(10^(4.1)(I_o))=10^(7.9-4.1)=10^(3.8) \\ =6309.573445 \\ \approx6310\text{ times as intense} \end{gathered}`

Answer;

`6310\text{ times as intense}`