Superlesson
Project 9-2

Advanced Algebra

Chapter 9, Exponential and Logarithmic Functions

In an effort to better understand the forces of the earth beneath us, seismologists--earthquake scientists--have gathered huge amounts of data on earthquakes.

Part B, Solving Exponential Equations

1. The Significant Earthquake Database contains information on more than 5000 destructive earthquakes that have occurred over the past 4000 years.

a. Search the database to find the Richter magnitudes of two quakes that took place in November, 1985--one in Turkey and one in the Vanuatu Islands.

b. The amplitude A of an earthquake shockwave is half the height of the wave. If R is the Richter magnitude of a quake and a is the amplitude of the normal background shockwave, R = log A / a. Let a = 1 unit.

Find the amplitudes of the Turkey and Vanuatu Islands earthquakes. Round to the nearest hundred.

c. Amplitude is a measure of the intensity of an earthquake. How many times stronger than the Turkey quake was the Vanuatu quake?

d. A quake approximately 200 times stronger than the Turkey quake took place in March, 1985. What was the Richter magnitude of the quake? In what group of islands did the quake take place?

Part D, Making Connections

2a. The formula log₁₀E = 11.4 + 1.5R approximates the amount of energy E in ergs, released in an earthquake of Richter magnitude R. Solve the formula for E.

b. The largest earthquake in U.S. history took place in Alaska on March 28, 1964. Find the Richter magnitude of the quake. Approximate the amount of energy released by the quake.

c. Look at the bottom of the page of the Largest Earthquakes in the United States to find out which earthquake released 2.5119 X10 ²³ ergs of energy. Which earthquake was it, and what was its magnitude?

d. The velocity v, in mi/h, at which a tsunami (tidal wave) travels is related to the depth d in ft of the water through which the wave travels by the formula log14.9d v = 0.5. Find the velocity of the tsunami unleashed by the 1964 Alaska earthquake as the wave traveled across Pacific Ocean waters 3 miles in depth.