Objective: To use logarithms in a real-life situation (using a cross-curricular setting)

Name:_________________ Algebra IIPer__________Earthquake ProjectObjective: To use logarithms in a real-life situation.

In 1935, American geologist Charles Richter defined the magnitude of an earthquake to be

SeverityScale

Richter

Mild0-4.3

Moderate4.3-4.8

Intermediate4.8-6.2

Severe6.2-7.3

Catastrophic7.3+

where M is the magnitude (as a decimal) I is the intensity of the earthquake (measured by the amplitude of a seismograph reading {measured in millimeters} taken 100 km from the epicenter of the earthquake) S is the intensity of a standard earthquake. The intensity of a standard earthquake (S) is 0.001 millimeters.

Because all earthquakes are compared to a standard earthquake, the magnitude of a standard earthquake is

Richter studied many earthquakes that occurred between 1900 and 1950. The largest had magnitude of 8.9 on the Richter scale, and the smallest had magnitude 0. This corresponds to a ratio of intensities of 800,000,000, so the Richter scale provides more manageable numbers to work with.

Each whole number increase on the Richter scale indicates an intensity ten times stronger. For example, an earthquake of magnitude 6 is ten times stronger than an earthquake of magnitude 5. An earthquake of magnitude 7 is 10 x 10 = 100times strong than an earthquake of magnitude 5. An earthquake of magnitude 8 is 10 x 10 x 10 = 1000times stronger than an earthquake of magnitude 5.Example 1:How much more intense is an earthquake of magnitude 6.5 on the Richter scale as one with a magnitude of 4.9?

Solution:The intensity (I) of each earthquake is different. LetI1represent the intensity of the stronger earthquake andI2represent the intensity of the weaker earthquake.

What you are looking for is the ratio of the intensities: So our task is to isolate this ratio from the above given information using the rules of logarithms.

Convert the logarithmic equation to an exponential equation.

The stronger earthquake was 40 times as intense as the weaker earthquake.

First Set of Problems:

1)Find the magnitude of the 1985 quake in Mexico City. It had a seismographic reading of 125,892 millimeters 100 kilometers from its epicenter.

2)Find the intensity of the 1906 San Francisco earthquake. It had an estimated magnitude of 8.3 on the Richter scale.

3)The 1989 Loma Prieta earthquake that shook San Francisco had a magnitude of 7.1 on the Richter scale. How many more times intense was the 1906 San Francisco earthquake than the 1989 event?

The Richter scale is quantitative logarithmic scale ScaleDescription

Richter

0-4.3Vibrations are recorded by instruments. People do not feel any Earth movement.

People at rest upstairs notice shaking. A few people might notice movement if they are at rest and/or on the upper floors of tall buildings.

Shaking felt indoors; hanging objects swing. Many people indoors feel movement. Hanging objects swing back and forth. People outdoors might not realize that an earthquake is occurring.

4.3-4.8Dishes rattle; standing cars rock; trees shake. Most people indoors feel movement. Hanging objects swing. Dishes, windows, and doors rattle. The earthquake feels like a heavy truck hitting the walls. A few people outdoors may feel movement. Parked cars rock.

Doors swing; liquid spills from glasses; sleepers awake. Almost everyone feels movement. Sleeping people are awakened. Doors swing open or close. Dishes are broken. Pictures on the wall move. Small objects move or are turned over. trees might shake. Liquids might spill out of open containers.

4.8-6.2People walk unsteadily; windows break; pictures fall off walls. Everyone feels movement. People have trouble walking. Objects fall from shelves. Pictures fall off walls. Furniture moves. Plaster in walls might crack. trees and bushes shake. Damage is slight in poorly built buildings. No structural damage.

Dificult to stand; plaster,bricks, and tiles fall; large bells ring. People have difficulty standing. Drivers feel their cars shaking. Some furniture breaks. Loose bricks fall from buildings. Damage is slight to moderate in well-built buildings; considerable in poorly built buildings.

6.2-7.3Car steering affected; chimneys fall; branches break; cracksin wet ground. Drivers have trouble steering. Houses that are not bolted down might shift on their foundations. Tall structures such as towers and chimneys might twist and fall. Well-built buildings suffer slight damage. Poorly built structures suffer severe damage. tree branches break. Hillsides might crack if the ground is wet. Water levels in wells might change.

General panic; damage to foundations; sand and mud bubble from ground. Well-built buildings suffer considerable damage. Houses that are not bolted down move off their foundations. Some underground pipes are broken. The ground cracks. Reservoirs suffer serious damage.

Most buildings destroyed; large landslides; water thrown out of rivers. Most buildings and their foundations are destroyed. Some bridges are destroyed. Dams are seriously damaged. Large landslides occur. Water is thrown on the banks of canals, rivers, lakes. The ground cracks in large areas. Railroad tracks are bent slightly.

7.3- +Railway tracks bend; roads break up; large cracks appear in ground; rocks fall. Most buildings collapse. Some bridges are destroyed. Large cracks appear in the ground. Underground pipelines are destroyed. Railroad tracks are badly bent.

Total destruction; "waves" seen on ground surface; river courses altered; vision distorted. Almost everything is destroyed. Objects are thrown into the air. The ground moves in waves or ripples. Large amounts of rock may move.

ON YOUR OWN:

Second Set of Problems: Graphing the Richter Scale

1)Graph the Richter Scale equation on each of the axes provided. (Use S = .001) {Your calculators will help you with this.} Pay attention to the scale on each x-axis

2)One of the strongest earthquakes ever recorded hit Haiti on January 12, 2010. It had a Richter scale rating of 8.8. Do you think there could ever be an earthquake with a rating of 12? Explain.

3)Suppose there was an earthquake that measured 12 on the Richter Scale. How many times more intense would a rating of 12 have to be compared to the 8.8 that struck Haiti? Show your work.