Exponential functions

Exponential functions describe processes where a quantity grows or shrinks at a rate proportional to its current size. Mathematically, they are expressed as \( y = a \times b^x \), where \( a \) is the starting amount and \( b \) is the growth (if \( b > 1 \)) or decay (if \( 0 < b < 1 \)) factor. These functions model many real-world phenomena such as population growth, radioactive decay, and investments with compound interest. As the input \( x \) increases, the output \( y \) either rapidly increases or decreases, reflecting accelerating changes over time.