Here's a function to compute the natural exponential function in arbitrary precision using the basic bcMath arithmetic operations.

EXAMPLE:
To compute the exponential function of 1.7 to 36 decimals:

$y = bcExp("1.7", 36);

The result:
4.331733759839529271053448625299468628

would be returned in variable $y

NOTE:
In practice, the last couple of digits may be inaccurate due to small rounding errors.  If you require a specific degree of precision, always compute 3-4 decimals beyond the required precision.

The program code for the natural exponential function is:
******************************************

  Function bcExp($xArg, $NumDecimals)

{
   $x = Trim($xArg);

   $PrevSum  = $x - 1;
   $CurrTerm = 1;
   $CurrSum  = bcAdd("1", $x, $NumDecimals);
   $n        = 1;

   While (bcComp($CurrSum, $PrevSum, $NumDecimals))

  {
   $PrevSum  = $CurrSum;
   $CurrTerm = bcDiv(bcMul($CurrTerm, $x, $NumDecimals), $n + 1, $NumDecimals);
   $CurrSum  = bcAdd($CurrSum, $CurrTerm, $NumDecimals);

   $n++;
  }

   Return $CurrSum;
}