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Logarithms

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Title: Logarithms


1

Logarithms
Wow! This is awesome!
2
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

3
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.

4
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.

5
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

6
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.

7
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.

8
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.

9
Natural Logarithms ( ln)
  • Natural logarithms are calculated in base e,
    which is also called the Euler number, named
    after Leonard Euler.

10
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

11
Amount of after 10 years at 5 interest.
12
Amount of after 10 years at 5 interest
13
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.

14
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
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