Exponential functions > Real exponents
12345Real exponents


With exponential growth you have to multiply by the same number every unit of time. This number is called the growth rate for that time unit. If g is the growth rate then: g > 0 .
To be able to use negative and/or rational exponents we need to agree about the following:

  • negative exponents: g - n = 1 g n

  • rational exponents: g 1 n = g n

These are valid for g > 0 and positive integer n .

Both completely fit in with the computational rules for powers, such as:
g - n = g 0 g n = 1 g n

This shows that a power g a for g > 0 is meaningful if the exponent a is either a positive number, a zero, a negative or a rational number.

The exponent a can be any real number in fact.
And that is why the graph of an exponential function can be drawn as smooth curves.

Here you see the graph of B = 6 2 t .

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