Final answer:
The attribute of big data associated with an exponential growth rate is known as exponential growth, involving data volumes that double at regular time intervals, resulting in a rapidly accelerating amount of data.
Step-by-step explanation:
The attribute of big data that involves an exponential data growth rate is referred to as exponential growth. This concept means that the volume of data is not just growing — it is growing at an accelerating pace. Each unit of time not only adds more data than the last but does so at a rate which is itself increasing.
For instance, if data volume doubles every two years, after the first period you would have 2x the original volume of data, then 4x, then 8x, and so forth. This is explained by an exponential model, which although simplistic, serves as a basis to understand growing phenomena where each step is a constant factor larger than the previous one. This type of growth is characterized by a pattern where after n time intervals (or doubling times), the increase is by a factor of 2 to the power of n (2n).