Exponents

Defn: N = b^ex or N = b^ex or N = b**ex
where N is the number, b is the base, often 10 but also e ( = 2.7183... Napier's constant), and ex is the exponent (or power term when an integer as in 10² is 10 to the power 2).

Note use of ^ (common calculator or single line format) or ** (common computer language format)

With the same base, exponents can be added or subtracted

For example; a^x x a^y = a^(x+y) to perform multiplication

or

a^x / a^y = a^(x-y) to perform division.

Some Example Calculations

b) 100 = e^4.605 = e^4.605 = e**4.605 where e = 2.7183 !!!

c) 10 x 100 = 10¹ x 10² = 10¹⁺² = 10³ = 1000

d) 10 x 100 = e^2.303 x e^4.605 = e^6.908 = 1000 when the base is the same you can add exponents to multiply numbers

Subtract exponents to divide

e) 5.6/1.2 = e^1.723 / e^0.182 = e^{1.723 - 0.182} = e^1.541 = 4.67

Use your calculator to check this answer

Table 2.2.1

x	0.0	0.5	1.0	1.5	2.0	2.5	3.0
10-x	1.000	0.316	0.100	0.032	0.010	0.003	0.001
e-x	1.000	0.607	0.368	0.223	0.135	0.082	0.050

Figure 2.2.1 Linear plot of 10^-x or e^-x versus x

Click on the figure to view the Java Applet window

• Exponential function at Wikipedia
• Exponential function at MathWorld
• Search for Exponential function at Goggle

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Copyright 2001-3 David W. A. Bourne (david@boomer.org)