Final answer:
The equation y = (0.37)^2x represents exponential decay with a percent rate of change of 63%. The base being less than 1 indicates the values of y decrease proportionally as x increases.
Step-by-step explanation:
The equation y = (0.37)^2x is an example of an exponential relationship where the variable x is in the exponent position, influencing the value of y. This equation represents a particular type of function known in mathematics as either an exponential growth or decay function, depending on the base of the exponent.
In this specific case, because the base of the exponent (0.37) is less than 1, the function represents an exponential decay. Each increase in the value of x results in the value of y becoming proportionally smaller. The percent rate of change, which can be determined by subtracting the base from 1 and converting it to a percentage (1 - 0.37 = 0.63), is therefore 63%, indicating a decrease.
Another way to understand this concept is to consider the rule of 70, which gives a quick estimation of doubling time based on a constant percentage rate of growth or decline. In the context of exponential growth or decay, time-series graphs are often used to represent data, showing the trend of the values over time.