Logarithmic Scales Lesson 4.4A

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

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

How to Graph These Numbers? Consider the vast range of the numbers Distance from the Sun Object Distance (million km) Mercury 58 Venus 108 Earth 149 Mars 228 Jupiter 778 Saturn 1426 Uranus 2869 Neptune 4495 Pluto 5900 Proxima Centauri 4.1E+07 Andromeda Galaxy 2.4E+13

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

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

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

Using Exponents to Indicate Distance Consider the following problem:  Given a number y ...   what value of x exists such that  x y -2 .. -1 0.01 .. 0.1  -1 .. 0 0.1 .. 1 0 .. 1 1 .. 10 1 .. 2 10 .. 100

Using Exponents to Indicate Distance Note the value we need to represent for Mercury's distance from the sun at 58 million kilometers, n, exponent 1.5 1.55 1.6 1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00 10n 31.62 35.48 39.81 44.67 50.12 56.23 63.10 70.79 79.43 893.1 100 Somewhere between these two For Mercury at 58 million km  58 = 101.76343

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