Application of Logarithmic Functions to Science MHF4UI Monday October 2 nd, 2012

The General Formula for Problems of Exponential Growth and Decay

Half-Life Example Homework 7.2 Part A Question 8 A 20-mg sample of thorium-233 decays to 17mg after 5 minutes. a)Determine the half-life of thorium-233.

Half-Life (Solution)

Application of Logarithmic Functions to Physical Sciences We can use Logarithmic functions in science to compare variables that occur over large orders of magnitude Said another way, we want a universal way to compare very small values to very large values Logarithmic Scales are often used in these types of situations. Some examples of Logarithmic Scales include: Decibel Scale Richter Scale pH Scale

Applications to of Logarithms to Sound

The Decibel Scale SoundDecibels Threshold of Hearing (TOH)0 dB Rustling Leaves10 dB Whisper20 dB Normal Conversation60 dB Busy Street Traffic70 dB Large Orchestra98 dB Front Rows of Rock Concert110 dB Threshold of Pain130 dB Military Jet Takeoff140 dB Instant Perforation of Eardrum160 dB Lung rupture200 dB

Decibel Scale Example 1

Decibel Scale Example 2 How many more times intense is the sound heard from the Front Rows Seats at a Rock Concert (110dB) vs. normal conversation (60dB)?

Applications to of Logarithms to Natural Disasters

March 11 th, 2011 Thousands of homes were destroyed, many roads were impassable, trains and buses were not running, and power and cellphones remained down.

Magnitude Scale Example The earthquake in Japan measured 8.9 on the Richter Scale. Compare this earthquake to the one that occurred in Leamington, Ontario that measured 3.0 on the Richter Scale.

Applications to of Logarithms to Chemistry AcidpH < 7 NeutralpH = 7 BasepH > 7

pH Scale Example 1

pH Scale Example 2

Homework Questions: Textbook Chapter 6.5 Part A: 1,2,6,7,8 Part B: 9,10,12