High School

The amount of energy \( E \) in ergs that an earthquake releases is related to its Richter scale magnitude by the equation:

\[
\log E = 11.8 + 1.5M
\]

Use the equation to find the amount of energy released by the 1960 Chilean earthquake, which measured 8.5 on the Richter scale.

Answer :

Final answer:

To calculate the energy released by the 1960 Chilean earthquake, substitute the magnitude of 8.5 into the equation logE = 11.8 + 1.5M to find logE = 24.55, which tells us the energy released is 10^24.55 ergs.

Explanation:

Calculating Earthquake Energy Release:

To find the amount of energy released by the 1960 Chilean earthquake that measured 8.5 on the Richter scale, we use the given equation logE = 11.8 + 1.5M, where M is the magnitude on the Richter scale. Substituting 8.5 for M, we get:

logE = 11.8 + 1.5(8.5)

logE = 11.8 + 12.75

logE = 24.55

To find the energy E in ergs, we must solve for E by using the property of logarithms:
E = 10^24.55

Therefore, the energy released by the 1960 Chilean earthquake is 10^24.55 ergs.