Answer
(a) The number $e$ is defined as the base of the exponential function such that its slope at the point $(0,1)$ is exactly equal to $1$.
(b) $e\approx2.718281828459\ldots$
(c)
$$f(x)=e^x.$$
Work Step by Step
(a) The number $e$ is defined as the base of the exponential function $f(x)=e^x$ such that its slope at the point $(0,1)$ is exactly equal to $1$.
(b) The approximate value of $e$ is $2.718281828459\ldots$
(c) The natural exponential function is the one with the basis equal to $e$:
$$f(x)=e^x.$$
