For 10 points, name this function that is the inverse of the natural logarithm function.
The moment-generating function of a random variable X is defined as the expectation value of this function of X times t. This function of x and this function of negative-x appear in the definition of the hyperbolic sine and cosine functions. The Taylor series of this function begins with the terms 1, x, and x-squared over 2. This function of i times theta is equal to cosine theta plus i sine theta, according to Euler's formula. This function, which is equal to its own derivative and antiderivative, can be used to model radioactive decay and continuously compounded interest. For 10 points, name this function that is the inverse of the natural logarithm function.
The moment-generating function of a random variable X is defined as the expectation value of this function of X times t.
exponential function [or e to the x or e to the negative -x and equivalents; or exponential growth or exponential decay; or exp x; or exp negative x; accept any variable in place of “x”]