Logarithms

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Logarithms
Wow! This is awesome!
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How do we use logarithms?

• pH level in blood
• slope of a beach
• speed of wind inside a tornado
• magnitude of an earthquake
• transport a substance into a human cell
• intensity of sound
• interest on money
• estimate the time of death

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pH level in blood.

• The pH of a patients blood can be calculated
  using the Henderson-Hasselbach Formula
• pH 6.1 log10 (B/C)
• where B is the concentration of bicarbonate, and
  C is the concentration of carbonic acid.

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Slope of a beach!

• The slope, s, of a beach is related to the
  average diameter, d (in millimeters), of the sand
  particles on the beach by the formula
• s0.159 0.118log10 d
• If the sand is very coarse, the slope of the
  beach will be steeper than if the sand is fine.

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Tornado!

• The speed of the wind, S (in miles per hour),
  near the center of a tornado is related to the
  distance the tornado traveled, d (in miles), by
  the formula
• S 93 log10 d 65

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Earthquake!

• The Richter scale is used to measure the
  magnitude, R, of an earthquake of intensity I is
  given by the formula
• R log10 I

• The intensity is a measure of the wave of energy
  of an earthquake per unit of area.

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Human Cells!

• The energy, E (in kilocalories per gram
  molecule), required to transport a substance from
  the outside to the inside of a living cell is
  given by the formula
• E 1.4(log C2 - log C1)

• C1 is the concentration of the substance outside
  the cell C2 is the concentration inside
  the cell.

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Sound !

• The level of sound, B (in decibels), is related
  to the intensity of the sound, I (in watts per
  square cm.), by the formula
• B 10 log10 (I/I0)

• I is the intensity of the faintest sound that can
  be heard by human ears.

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Natural Logarithms ( ln)

• Natural logarithms are calculated in base e,
  which is also called the Euler number, named
  after Leonard Euler.

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Interest on MONEY!

• If interest is compounded quarterly, use the
  formula
• A P( 1 r / n ) nt

• If interest is compounded continuously, use the
  formula
• A Pe rt

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Amount of after 10 years at 5 interest.
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Amount of after 10 years at 5 interest
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Time of Death!

• To estimate the time of death of a human body, a
  coroner uses Newtons law of cooling
• Kt ln(T-S)/(T0-S1)

• k is a constant, S is the temperature of the
  surrounding air, t is the time it takes for the
  body temperature to cool from the time of death.

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Credits

• Algebra 2, An Integrated Approach,D.C. Heath and
  Company
• Microsoft clip-art and pictures
• Stribling Funeral Home
• http//www.animfactory.com/
• http//wwwpersonal.engin.umich.edu/dkyser/weather
  /pics.htm
• Encyclopedia of World Biography, 2nd edition,
  Diderot and Forbes, 1998