Final answer:
Without the explicit form of the function, determining if it's exponential is not possible. If given a function like f(x) = (4/7)x or f(x) = (7/4)x, these would be exponential functions with bases 4/7 and 7/4 respectively. Exponential functions are defined by having the variable in the exponent. (Option A).
Step-by-step explanation:
To determine whether the given function is exponential, we need to know its form. An exponential function typically takes the form f(x) = ax, where 'a' is the base and is a positive real number, not equal to 1, and 'x' is the exponent that can be any real number. Exponential growth features the variable as the exponent, and it scales as the power of the base raised to the time interval.
For instance, if the function is f(x) = (4/7)x, then it is exponential with a base of 4/7. If it's f(x) = (7/4)x, the base is 7/4. In such cases, we use exponential arithmetic to manage calculations involving these functions, and the natural logarithm (ln) as it is an inverse operation to the exponential function, enabling us to convert between forms and solve equations involving exponentials.
If the function does not have a variable as the exponent, then it's not an exponential function. Without the specifics of the function's form, we can't affirm if it is exponential or identify the base. Assuming an exponential form, options A and B each describe an exponential function with the given base, but we need the exact function to select the correct answer.