Final answer:
The equation y=16(0.75)^x represents an exponential decay function, where y approaches zero as x approaches infinity.
Step-by-step explanation:
The equation in question, y=16(0.75)^x, represents an exponential decay function. In this type of function, as x increases or approaches infinity (x → ∞), the value of y will decrease towards zero. This happens because any number less than 1 raised to an increasingly large exponent will get closer and closer to 0. Therefore, the limit of y as x approaches infinity is 0.
The behavior of this function is an important concept in mathematics as it illustrates how exponential functions can model decay processes in various fields such as physics, biology, and finance. For instance, the decay in radioactive substances or the depreciation of a car's value over time can be modeled using similar exponential decay functions.