I don't see how the reference to ieee.math_real.exp answers the question for calculate exponential in FPGA, because it's not synthesizable.
You can of course use math_real to calculate a lookup table, or implement the power series calculation used in math_real body in a sequential algorithm. But you should suggest the solution explicitly then.
Lookup table with linear piecewise interpolation would be my first choice.
Not sure about the question. Lookup table is synthesizable. It has been often suggested at Edaboard for the implementation of various functions in FPGA.