Logarithmic scale: Richter scale (earthquake)

Logarithmic scale: Richter scale (earthquake)

We have previously learnt that applying logarithm on a humungous number will give us a much smaller number. Ever wondered how this property can help us in our daily lives? One of the many applications of logarithmic properties is to measure the magnitude of earthquakes, which we call the Richter magnitude scale. In this section, we will explore the concept of this logarithmic scale and its applications.
Basic concepts: Exponents: Division rule axay=a(x−y){a^x \over a^y}=a^{(x-y)},
Related concepts: Derivative of inverse trigonometric functions, Derivative of logarithmic functions,

Lessons

  • 1.
    The 2011 earthquake in Japan measured 9.0 on the Richter scale.
    The 2008 earthquake in China measured 7.9 on the Richter scale.
    Complete the following 2 sentences:
    (i) The Japan earthquake was __________ times as intense as the China
    earthquake.

    (ii) The China earthquake was __________ times as intense as the Japan
    earthquake.
  • 2.
    Earthquake "Alpha" measured 5.8 on the Richter scale.
    Earthquake "Beta" was 200 times as intense as Earthquake "Alpha".
    Earthquake "Gamma" was 11000 { 1\over 1000 } times as intense as Earthquake "Alpha".
    What was the Richter scale readings for:
    (i) Earthquake "Beta"
    (ii) Earthquake "Gamma".
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9.
Applications of Exponential and Logarithmic Functions
9.1
Exponential growth and decay by a factor
9.2
Exponential decay: Half-life
9.3
Exponential growth and decay by percentage
9.4
Finance: Compound interest
9.5
Continuous growth and decay
9.6
Logarithmic scale: Richter scale (earthquake)
9.7
Logarithmic scale: pH scale
9.8
Logarithmic scale: dB scale
9.9
Finance: Future value and present value
Grade 12 Math
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