1. Section 4.4 Logarithmic Scales

2. 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

3. What we have created is a logarithmic scale
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

4. 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

5. 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
6510
8.78

6. In your groups try problems 12 and 15