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Section 4.4 Logarithmic Scales. Plot the distances on a number line. If you haven’t already, try plotting the data on an axis labeled 10 0 , 10 1 , 10 2 , 10 3 , and so on How do you decide where to put each planet on this scale? Can we fit all the planets now? - PowerPoint PPT Presentation
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Section 4.4Logarithmic Scales
Plot the distances on a number lineObject 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
• If you haven’t 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
xxy y 10thenlogIf
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
• 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
• In your groups try problems 12 and 15