Section 4.4 Logarithmic Scales

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Section 4.4Logarithmic Scales
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Plot the distances on a number line
Object Distance (million km)
Mercury 58
Venus 108
Earth 149
Mars 228
Jupiter 778
Saturn 1426
Uranus 2869
Neptune 4495
Pluto 5900
Proxima Centauri 4.1 x 107
Andromeda Galaxy 2.4 x 1013
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• If you havent already, try plotting the data on
  an axis labeled 100, 101, 102, 103, and so on
• How do you decide where to put each planet on
  this scale?
• Can we fit all the planets now?
• In order to fit all the planets on this scale you
  must convert their distances to powers of 10
• How do we do this?
• Recall
• What we have created is a logarithmic scale

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Use of logs to fit an exponential function to data

• Consider the following table of data
• Create a scatter plot with your calculator
• What form does the data have?

x y
1 210
2 405
3 833
4 1590
5 3245
6 6510
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• We can use logarithms to make this data linear
• Make a scatter plot of x vs. ln(y)
• How does the data look?
• Find both the exponential and linear regression
  functions

x y ln(y)
1 210 5.34
2 405 6
3 833 6.72
4 1590 7.37
5 3245 8.08
6 6510 8.78
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• In your groups try problems 12 and 15