Compare and Contrast Linear and Exponential Functions? - Answers

Linear functions have a constant rate of change, represented by a straight line on a graph, and can be expressed in the form (y = mx + b), where (m) is the slope and (b) is the y-intercept. In contrast, exponential functions increase (or decrease) at a rate proportional to their current value, leading to a curve that rises or falls steeply, often represented as (y = ab^x), where (a) is a constant and (b) is the base of the exponential. While linear functions grow by equal increments, exponential functions exhibit growth (or decay) that accelerates over time. This fundamental difference in growth behavior makes exponential functions particularly significant in modeling phenomena like population growth or compound interest.