1. Logarithmic Scales Lesson 4.4A

2. Graphing Difficult Data Some data can be easily considered on a linear scale:  Weights of a team of football players  Heights of a team of volleyball players  GPA's of a class of students

3. Graphing Difficult Data Other things are more difficult to represent on a linear graph due to the vast range of values There are data of several orders of magnitude Examples  distance to the moon, to planets  light brightness  loudness of a sound

4. How to Graph These Numbers? Consider the vast range of the numbers Distance from the Sun ObjectDistance (million km) Mercury58 Venus108 Earth149 Mars228 Jupiter778 Saturn1426 Uranus2869 Neptune4495 Pluto5900 Proxima Centauri4.1E+07 Andromeda Galaxy2.4E+13

5. How to Graph These Numbers? What's wrong with this picture?

6. How to Graph These Numbers? What's wrong with this picture? We need a way to set a scale that fits all the data

7. How to Graph These Numbers? The solution: Set the scale to be the exponent of the distance This is called a logarithmic scale

8. Using Exponents to Indicate Distance Consider the following problem:  Given a number y... what value of x exists such that xy -2.. -10.01.. 0.1 -1.. 00.1.. 1 0.. 11.. 10 1.. 210.. 100

9. Using Exponents to Indicate Distance Note the value we need to represent for Mercury's distance from the sun at 58 million kilometers, n, expo nent 1.51.551.61.651.701.751.801.851.901.952.00 10 n 31.6235.4839.8144.6750.1256.2363.1070.7979.43893.1100 Somewhere between these two For Mercury at 58 million km 58 = 10 1.76343

10. Assignment Lesson 4.4A Page 181 Exercises  1 – 5, 9, 11, 13, 15