The Exponential Function and Its Applications

General Mathematics — Second Secondary

Growth, decay and the graph

Comparison aspect	Main idea	Keywords
If a > 1	the function is increasing on the real numbers and models growth, for example f(x) = 2^x.	functionincreasingrealnumbers
If 0 < a < 1	the function is decreasing on the real numbers and models decay, for example f(x) = (1/2)^x.	functiondecreasingrealnumbers
•	Table of values for f(x) = 2^x:	Tablevalues

x	−2	−1	0	1	2	3
f(x)	1/4	1/2	1	2	4	8

From the table, the graph always passes through (0, 1), and the x-axis (y = 0) is a horizontal asymptote.
The curve gets closer and closer to this line without touching it.
Useful exponent laws a0 = 1, ax + y = ax × ay, and a−x = 1 / ax.

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