Chapter 4.5, Problem 4E

Reminder Round all answers to two decimal places unless otherwise indicated.

Magnitude and Energy The magnitude $M$ of an earthquake is related to the energy $E$ that it releases.The formula is

$M=\frac{\log E+7.5}{1.5}$.

Here the unit of energy is the terajoule, which is one trillion joules. One joule is approximately the energy expended in lifting $3/4$ of a pound one foot. One terajoule is approximately the energy produced by burning one million cubic feet of natural gas.

a.What is the magnitude of a $10\text{-terajoule}$ earthquake? Round your answer to one decimal place.

b.On September 24, 2013, a quake of magnitude $7.7$ struck Pakistan. How much energy was released by that quake?

c.The atomic bomb dropped on Hiroshima released about $60\text{terajoules}$ of energy. How many such bombs would be needed to produce the energy released by the Pakistan quake from part b? Round your answer to the nearest whole number.