Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.

Exponential functions can indicate either growth or decay based on the base of the exponent. If the base is greater than 1, the function represents growth; if it is between 0 and 1, it represents decay. To determine the percentage rate, you can use the formula \( r = (b - 1) \times 100 \), where \( b \) is the base of the exponential function. For instance, if the function is \( f(x) = 3^x \), it shows growth, and the percentage rate of increase is \( (3 - 1) \times 100 = 200\% \). Conversely, for \( f(x) = 0.5^x \), it signifies decay with a percentage rate of decrease of \( (0.5 - 1) \times 100 = -50\% \). If you need practical examples and visualizations, consider graphing these functions using software or graphing calculators—they offer fantastic insights into how the function behaves over time! You’ll see the sharp climb of growth functions and the graceful decline of decay functions, making it easier to grasp these concepts visually.