Question

Determine if the function f is an exponential function. If so, identify the base. If not, why not?

f(x)=(1/e)^x


A. This is not an exponential function because the variable is in the exponent position.


B. The base is x.


C. This is a polynomial.


D. The base is e^−1.

Answer 1

Answer: D) The base is e^(-1)

We use the rule that x^(-k) = 1/(x^k). That allows us to say e^(-1) = 1/(e^1) = 1/e

The 1/e is the base of the exponential (1/e)^x

In general, the exponential b^x has base b.