Exponential models and exponential relationships. Are they the same thing?

Question

Are exponential models the same as exponential relashionships?

Answer 1

Kind of. Obviously, both deal with exponential growth, and I think if you were in a 'casual' conversation about math, you would be able to use the two interchangeably and they would both be understood. However, there is a small difference between "model" and "relationship". An exponential "model" would likelier occur when you have data that you collected and measured. If you measured the number of fish in a pond and realized that the growth of the fish follows an exponential curve, the growth of fish would be an exponential model. However, an "exponential relationship" is slightly different in that an exponential relationship is exact. If we talk about the intensity of sound, the formula is Intensity=Watts/meter². When the listener is x meters away from the sound source, the intensity of the sound decreases by x² meters. An exponential relationship is mathematically proven by a formula, while an exponential model follows a trend that happens to be an exponential curve.