Final answer:
The base 'b' of the exponential model given by the equation n = 20.5 (0.6394)^t is 0.6394, which indicates an exponential decay since it is less than 1.
Step-by-step explanation:
The equation given is n = 20.5 (0.6394)^t, and we need to determine the base of the exponential model and whether it represents a growth or decay factor. The exponential equation is typically written in the form of n = a(b)^t, where 'a' is the initial amount, 'b' is the base, and 't' is the time. In the given equation, the base 'b' is 0.6394. Since the base is less than 1, it indicates an exponential decay. To confirm, if we plug in positive values for 't', the overall value of the equation decreases, which is characteristic of decay rather than growth.
The importance of identifying whether the factor represents growth or decay is crucial. For example, in an application where the base is more than 1, like a population growing by 5% annually, we could use the base of 1.05 to represent a growth factor. On the other hand, if we wanted to model something that halves over time, the base would be less than 1, indicating a decay.