What is an exponential curve?

An exponential curve represents a mathematical function where the rate of change is proportional to the current value, leading to rapid growth or decay. Typically expressed in the form (y = a \cdot e^{bx}), where (e) is the base of natural logarithms, (a) is a constant, and (b) determines the growth (positive (b)) or decay (negative (b)). This type of curve is commonly seen in phenomena such as population growth, radioactive decay, and compound interest. The key characteristic is that as the value increases, the growth rate accelerates, resulting in a steep rise or fall.