Since this property cannot be animated or driven, the only thing left is to control it with script:
import bpy
import math
def function(frame):
# modify this function if you want
return math.pow(4.75, (frame-30)/50) - 0.75
def my_handler(scene):
# this code will be run on every frame change
scene.render.motion_blur_shutter = function(scene.frame_current)
bpy.app.handlers.frame_change_pre.append(my_handler)
Run this in the Text editor, render the animation normally.
If you want to make changes after you ran the code, remove the handler first with typing this into the console: bpy.app.handlers.frame_change_pre.clear()
If you would like to animate the value, create a custom ID property for the scene which you can animate (name the property "shutter"):

And use this code (it copies the value into the shutter speed):
import bpy
def my_handler(scene):
scene.render.motion_blur_shutter = scene["shutter"]
bpy.app.handlers.frame_change_pre.append(my_handler)
for t in frameRange { set shutter = function(t); render frame to image; }
$\endgroup$