Linear Interpolation

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(Linear) Interpolation
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• To determine the value a/b of the way from l to
  u, compute the following

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Example

• What value is 3/5ths of the way from 18 to 33?
• Here a 3 and b 5, l 18 and u 33.

The distance from 18 to 33 is 15. Start at 18 and
go 3/5 0.60 times 60 of the distance of 15
from 18 to 33.
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• What value is 3/5ths of the way from 18 to 33?
• What value is 0.60 of the way from 18 to 33?
• What value is 60 of the way from 18 to
  33?----------------------------------------------
  -------------

What value is 40 of the way from 33 to 18?
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Applying Linear Interpolation

• In the previous two quarters a company made a
  profit of 700,000 on sales of 410 units, and a
  profit of 1,200,000 on sales of 635 units.
• The companys forecast for the next quarter is
  sales of 575 units. Use linear interpolation to
  anticipate the companys profit for the next
  quarter.

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• In the previous two quarters a company made a
  profit of 700,000 on sales of 410 units, and a
  profit of 1,200,000 on sales of 635 units.
• The companys forecast for the next quarter is
  sales of 575 units. Use linear interpolation to
  anticipate the companys profit for the next
  quarter.
• Begin by setting up a table

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• 575 is 165/225 0.7333 (73.33) of the way from
  410 to 635.
• So Determine the profit that is 165/225 0.7333
  of the way from 0.7 to 1.2

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• Determine the profit that is 165/225 0.7333 of
  the way from 0.7 to 1.2
• Profit 0.7 0.7333(1.2 0.7)
• 0.7 0.7333(0.5)
• 1.0667
• Using linear interpolation we anticipate a profit
  of 1,066,667.

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Example

• A car on a test track gets 34.5 miles per gallon
  (mpg) when traveling at a speed of 50 miles per
  hour (mph), and 38.0 mpg when going 60 mph. What
  mileage is anticipated at 55 mph? Use linear
  interpolation to anticipate the mileage at a
  speed of 55 mph.
• 34.5 0.5(3.5) 36.25 mpg

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