Question

The 1985 Mexico City earthquake measured a magnitude 8.0 on the Richter scale. The Richter scale uses the function M (I) = log (StartFraction I Over I Subscript 0 Baseline EndFraction). Which equation relates the intensity of the 1985 earthquake, I, with the intensity of the threshold quake, Io?
A.) I = 810(Io)

B.) Io = 810(I)

C.) I = 108(Io)

D.) Io = 108(I)

Answer 1

Answer:

The correct option is C: I = 10⁸I₀.   

Step-by-step explanation:

The function of the Richter scale is:

$M_{(I)} = log(\frac{I}{I_{0}})$

Since the magnitude of the earthquake is 8.0, the relation between the intensity, I, with the intensity of the threshold quake, Io, is:

$8.0 = log(\frac{I}{I_{0}})$

$10^{8} = \frac{I}{I_{0}}$

$I = 10^{8}I_{0}$

Therefore, the correct option is C: I = 10⁸I₀.                

I hope it helps you!