Chapter 3.5, Problem 49E

(a)

To determine

To calculate: The expression of $I$ in terms of $I_0$ for magnitude 7 on the Richter scale, when the intensity of earthquake is given by $I=I_0\cdot {10}^R$.

(b)

To determine

To calculate: The expression of $I$ in terms of $I_0$ for magnitude 8 on the Richter scale, when the intensity of earthquake is given by $I=I_0\cdot {10}^R$.

(c)

To determine

The comparison between intensities, $I=I_0\cdot {10}^7$ and $I=I_0\cdot {10}^8$ obtained in part (a) and part (b) respectively.

(d)

To determine

To calculate: The rate of change $\frac{dI}{dR}$, when the intensity of earthquake is given by $I=I_0\cdot {10}^R$.

(e)

To determine

The meaning of $\frac{dI}{dR}$ which is $\frac{dI}{dR}=I_0\cdot \ln 10\cdot \left({10}^R\right)$ calculated in part (d).