How does an exponential function change when its base is between 0 and 1?

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A graph of the function f(x) = x cubed minus 3x plus 2 is shown on a blue background, with a red curve passing through key points. Local maximum and minimum points are marked with black dots at x equals negative 1 and x equals 1, illustrating important features of the curve. — function Plot of the cubic equation f(x) = x³ − 3x + 2. The plotted points are where changes in curvature occur.

In mathematics, an exponential function is defined by the relation $y = a^{x}$ , where $a$ is a positive real number not equal to 1.

When the base $a$ is between 0 and 1 (i.e., $0 < a < 1$ ), the function is strictly decreasing as $x$ increases. Rather than representing exponential growth, this behavior characterizes exponential decay. For instance, the function $y = (1 / 2)^{x}$ demonstrates this property, as its value diminishes toward zero as the exponent $x$ grows larger.1