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Definition:
Note use of ^ (common calculator or single line format) or ** (common computer language format) for general exponentiation. Exponents with base e may also be expressed as exp(x) [= e^{x}] (a commom computer function 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.
b) 100 = e^{4.605} = e^4.605 = e**4.605 where e = 2.7183 !!!
c) 10 x 100 = 10^{1} x 10^{2} = 10^{1+2} = 10^{3} = 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 interactive graph
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