Final answer:
The exponential function grows at a rate proportional to its current value, leading to a rapid increase over time compared to the steady, constant rate of a linear function.
Step-by-step explanation:
The exponential function exceeds the linear function because its growth rate increases over time, proportional to the current value. In contrast, a linear function grows at a constant rate. Exponential growth is characterized by the equation y = a × bn, where a is the initial amount, b is the growth factor, and n is the number of time intervals. For example, if we have a doubling situation (b=2), after n time intervals, the growth is by a factor of 2n. This pattern of growth results in an exponential curve that skyrockets relative to the steady increase of a linear graph. This concept is evident in phenomena like the exponential increase in bacteria population or the relationship between vapor pressure and temperature where the amount or effect multiplies over each time period.