While i am sure you have a reason to use the older version of Blender (update is much recommended though).
That said, you should be able to get it done by doing the following:
- Go to frame 1, where the scale is supposed to be 0.001
- Enter the value of 0.001 and then with the mouse over the scale field, press I to set a keyframe for that attribute at frame 1.
- Now jump to frame 300 and enter the new value (0.05) for the scale and again with the mouse over the scale field press I to set another keyframe.
If you now play the animation, the scale value will be interpolated between 0.001 and 0.05 over the run of 300 frames. If you want a linear interpolation, you need to go in the graph editor and under key menu -> Interpolation Mode -> Linear. Or just press T and select Linear, like in the picture below.
I packed all in a little visual demonstration: