# How do you tell whether f(x)=(5/6)^x is an exponential growth or decay?

Dec 15, 2017

Values greater than one raised to a power give growth, 0 < z < 1 are decay

#### Explanation:

Exponents are simply a shorthand version of multiplication. Imagine multiplying 1/2 by 1/2 again and again. Your answer will continue to get smaller.

Now imagine multiplying 2 times 2 again and again. Your answer will continue to increase.

So x < 0 < 1 leads to decay

x > 1 leads to growth

Side note: x = 0 gives a result of 1, since anything to the zero power is 1. x = 1 just gives the original value.