Write a program to compute the value of the mathmatical constant e to the power of x $($ex$)$ and the number of terms used to compute it using the following infinite series:

ex $=1+$ x$/1!+$ x$2/2!+$ x$3/3!+$ x$4/4!+...$

Your program should include at least one function called compute$\_$ex which receives any value of x as a parameter and returns the following two values:

$1)$ Value of ex for the given x$.$

$2)$ The number of terms used in computing ex$.$

The computation should stop when the new term added $($ term $=$ Xn$/$n$!$ where n$=0,1,2,3,...)$ is less than $0\mathrm{.}0001.$

Your program should also NOT use the already predefined system function pow or use your own pow and factorial functions. You should solve the equation as a series and NOT by calling pow and factorial functions.