APPLICATIONS OF EXPONENTIAL | |

AND | |

LOGARITHMIC FUNCTIONS |

**EARTHQUAKE WORD PROBLEMS:**

As with any word problem, the trick is convert a narrative statement
or question to a mathematical statement.

Before we start, let's talk about earthquakes and how we measure their
intensity.

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

where I is the intensity of the earthquake (measured by the amplitude of a seismograph reading taken 100 km from the epicenter of the earthquake) and S is the intensity of a ''standard earthquake'' (whose amplitude is 1 micron =10

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 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
times strong than an earthquake of magnitude 5. An earthquake of
magnitude 8 is
times stronger than an earthquake
of magnitude 5.

**Example 1:**

**Solution:**

Convert the second sentence to an equivalent mathematical sentence or
equation.

Solve for

The intensity of the earthquake in South America was 8.9 on the Richter scale.

**Example 2:**

**Solution:***I*_{1} represent the intensity the early earthquake and *I*_{2}represent the latest 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 early earthquake was 16 times as intense as the later earthquake.

If you would like to test your knowledge by working some problems, click on
problem.

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