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Cycle 2 - Lesson 5 Logarithmic Functions - Modelling and Applications General equation for Logarithmic Functions used for modeling:

f ( x) = a log[k ( x − d )] + c

A logarithmic scale is a nonlinear scale used when there is a large range of quantities. Common uses include the earthquake strength, sound loudness, light intensity, and pH of solutions. It is based on orders of magnitude, rather than a standard linear scale, so each mark on the scale is the previous mark multiplied by a value.

Application #1 of Modelling with Logarithms – Richter scale for earthquakes

Descriptor

Richter Magnitude

Damage caused by the earthquake

Frequency of occurrence

Micro

Less than 2.0

Micro (very small) earthquakes, people cannot feel these.

About 8,000 each day

Very minor

2.0-2.9

People do not feel these, but seismographs are able to detect them.

About 1,000 per day

Minor

3.0-3.9

People often feel these, but they rarely cause damage.

About 49,000 each year

Light

4.0-4.9

Objects inside houses are disturbed, causing noise. Nothing is damaged.

About 6,200 each year

Moderate

5.0-5.9

Buildings that are not built well may be damaged. Light objects inside a house may be moved.

About 800 per year

Strong

6.0-6.9

Moderately powerful. May cause a lot of damage in a larger area.

About 120 per year

Major

7.0-7.9

Can damage things seriously over larger areas.

About 18 per year

Great

8.0-9.9

Massive damage is caused. Heavy objects are thrown into the air and cracks appear on the ground, as well as visible shockwaves. Overhead highways may be destroyed, and buildings are toppled.

About 1 per 20 years

Meteoric

10.0+

There are no records of anything of this size. The vibration is about the same as that of a 15 mi meteor.

Unknown

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Each whole number increase on the Richter scale indicates an intensity 10 times stronger. For example, an earthquake of magnitude 6 is 10 times stronger than an earthquake of magnitude 5. An earthquake of magnitude 7 is than an earthquake of magnitude 5.

times stronger

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

a)

Write the magnitude equation in exponential form.

b)

In 2010, Haiti experienced an earthquake of magnitude 7.0. In 2011, the earthquake off the coast of Japan was 100 times stronger than the one in Haiti. What was the magnitude of the large earthquake in Japan?

c)

The strongest earthquake in recorded history took place in Chile in 1960, causing a tsunami that affected countries on the opposite side of the Pacific Ocean.That earthquake had a magnitude of 9.5. The strongest earthquake that has occurred in Burlington, Ontario occurred in 1983 and had a magnitude of 3.1. How many times stronger was the earthquake in Chile than the one in Burlington?

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Application #2 of Modelling with Logarithms – pH Scale

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Application #3 of Modelling with Logarithms – Decibel Scale

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C2-L5 - Practice Questions – Applications of Logarithms 5.

6.

3.

Optional:

4.

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ANSWERS to Practice Questions

3. 4. 5. 6.