by what approximate factor is the intensity of an earthquake with magnitude 5.4 greater than an earthquake…

by what approximate factor is the intensity of an earthquake with magnitude 5.4 greater than an earthquake with magnitude 5.3?\nm = logleft(\frac{i}{i_0}\right)\n$m$ = the magnitude of an earthquake\n$i$ = the intensity of an earthquake\n$i_0$ = the smallest seismic activity that can be measured, which is 1\n1.01\n1.21\n1.26\n10.44

by what approximate factor is the intensity of an earthquake with magnitude 5.4 greater than an earthquake with magnitude 5.3?\nm = logleft(\frac{i}{i_0}\right)\n$m$ = the magnitude of an earthquake\n$i$ = the intensity of an earthquake\n$i_0$ = the smallest seismic activity that can be measured, which is 1\n1.01\n1.21\n1.26\n10.44

Answer

Explanation:

Step1: Write equations for each magnitude

For magnitude $M_1 = 5.3$, we have $5.3=\log\left(\frac{I_1}{I_0}\right)$. Since $I_0 = 1$, then $I_1 = 10^{5.3}$. For magnitude $M_2=5.4$, we have $5.4=\log\left(\frac{I_2}{I_0}\right)$. Since $I_0 = 1$, then $I_2 = 10^{5.4}$.

Step2: Find the ratio of intensities

The ratio $\frac{I_2}{I_1}=\frac{10^{5.4}}{10^{5.3}}$. Using the rule of exponents $\frac{a^m}{a^n}=a^{m - n}$, we get $\frac{I_2}{I_1}=10^{5.4 - 5.3}=10^{0.1}$.

Step3: Calculate the value of $10^{0.1}$

$10^{0.1}\approx1.26$.

Answer:

C. 1.26