Solving Equations'''

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Solving Equations...

• Carbon-14 Dating
• Process used to estimate how long since
  something died.
• It is only an estimate...

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Over 5000 years ago, a man climbed up to the icy
heights of the Schnalstal glacier and died. He
was found by accident in 1991, with his clothes
and equipment, mummified and frozen an
archaeological sensation and a unique snapshot of
a Copper Age man.
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The Man in the Ice

• In September 1991, Erika and Helmut Simon were
  walking in the Alps near the Austrian border with
  Italy, when they came upon the body of a dead
  mountaineer. Only the head was visible above the
  ice.
• The good preservation of the body, clothes and
  implements gives a fascinating glimpse of what
  life might have been like for a person living in
  Neolithic times in Ireland.

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• The following items were found
• An axe with a copper blade and yew shaft
• A bow and a quiver of arrows, flint arrow heads
• A small dagger in a scabbard
• A back pannier made of hazel rods, larch boards
  and birch bark
• Other smaller items, such as cords and flints
• Fragments of the iceman's clothes were also
  found, and they are well enough preserved to be
  able to see different types of stitching used for
  temporary repairs, presumably by the iceman
  himself. They included
• A fur cap
• A upper garment made of pieces of fur sewn
  together
• Fur leggings held up by a belt
• A soft leather loincloth
• Leather shoes, with a inner net of grass cords

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• Examination of the body allowed a possible
  reconstruction of the last hours of this man's
  life. The Neolithic people were farmers, growing
  varieties of wheat and barley. Two grains of
  barley and some wheat chaff were found in the
  iceman's clothing. They had domesticated animals
  (such as dogs, goats, pigs and cattle) and hunted
  wild animals such as ibex, deer and birds.

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• Konrad Spindler thinks that the iceman may have
  been a shepherd, accustomed to living for several
  months away from the settled community hunting
  for food and to protect the herd. He may have
  returned to his community to find that some
  disaster had occurred (perhaps a violent attack,
  since he had four broken ribs) and fled over the
  mountain pass. Tired and hungry, he laid down his
  axe, bow and backpack on a rock ledge, and lay
  down to rest. He never woke up.

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• Suspicions that the body might be very much older
  were confirmed by Konrad Spindler. He examined
  the body, the "ice-pick" and other items found
  with the body. He concluded that the axe was
  either early bronze age or late Neolithic, and
  therefore that the body was at least 4000 years
  old. (It was later dated as late Neolithic, or
  about 5000 years old).

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FORMULA

• A(t)A0(0.883)t
• A(t)Amount of C-14 present t thousand years
  after death.
• A0 Amount C-14 at death.
• t time in 1000 years.

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SOLVING

• Remember, when solving equations, as long as you
  perform an operation on Both Sides, it is legal.

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Sample

• A bison bone found in 1968 contained 37 of the
  C-14 present when the bison died. Estimate the
  age of the bone.
• The bone is about 8000 years old.

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Try this...

• A bone found contained 48 of the C-14 present
  when an animal died.
• Estimate the age of the bone.
• approximately 6000 years.

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What about logs?

• Solve for X
• log4 x log4 (x-6) 2
• Remember CHECK!!!
• Answer X 8

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Try another!

• Solve for X
• log2 x log2 (x-2) 3
• Answer X 4

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Try these...

• 3x 4
• 9x-4 6.28
• 2log2 x - log2 (x3) 2
• log7 (m1) 1 - log7 (m-5)
• x1.26,x4.836 , x6, m6

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Assignment

• Page 320 1-16, 25-29
• Chapter Review page 324-327
• Extra Practice Page 615-617