Final answer:
The base b of an exponential function should be positive to ensure the function is well-defined for all real number inputs and reflects consistent growth patterns, such as in a doubling sequence represented by 2^n.
Step-by-step explanation:
For the exponential function f(x) = c · b^x, the base b should be positive because only positive bases ensure the function remains well-defined for all real numbers x. Negative bases can cause issues with non-integer exponents leading to complex or undefined values. In the context of exponential growth, this positivity ensures that the function reflects a consistent growth pattern over time, as exemplified by the doubling sequence (2^x) where the base 2 is positive. In this scenario, after n doubling times, we have increased by a factor of 2^n.