An exponential curve is a type of exponential function that produces a curve that continuously increases or decreases at an increasing rate. There are several synonyms for this term, including exponential growth, exponential decay, exponential rise, and exponential increase.
Another similar term is "geometric progression", which refers to a pattern of growth or increase where each term is multiplied by a fixed ratio. Additionally, the terms "hyperbolic curve" or "hyperbolic function" may also be used to describe a similar type of curve that approaches but does not reach an asymptote. Regardless of the specific synonym used, these terms all describe a pattern of rapid growth or decay that can be modeled mathematically through the use of exponential functions or other mathematical tools.