Did you know that exponential functions like grow at an increasing rate as increases? This means that even small changes in can lead to larger and larger increases in . For instance, if you evaluate and , you’ll see how quickly it starts to rise: and .

In real-world applications, exponential functions can model various phenomena, such as population growth, radioactive decay, and even finance through compound interest. In investments, for example, if you invest money with a growth rate similar to , you can expect your investment to grow significantly over time, making it essential to understand these functions for financial planning.