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How does an exponential function change when its base is greater than 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 fixed positive real number other than 1.

When the base $a$ is greater than 1, the function is increasing. This behavior represents exponential growth, where the value of the function rises as the variable $x$ increases. Conversely, if the base is between 0 and 1, the function is decreasing, representing exponential decay. If the base were equal to 1, the function would be constant, showing neither growth nor decay.12