Exponential growth and decay bridge
An exponential function like y = a(1+r)^t models growth or decay by a constant percent rate each time period, growing or shrinking by equal factors over equal intervals, unlike a linear function that changes by a constant amount over equal intervals: for example, y = 100(1.05)^t models an investment starting at 100 and growing 5% every period, so after 1 year, y = 100(1.05) = 105. Here a is the starting value and r is the growth or decay rate, and a growing exponential function eventually outgrows any linear or quadratic function, no matter how big their own rates are, while a decaying one instead shrinks toward zero.
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