Smoothly Interpolate Values Relating To Camera Angle?

So effectively I have a camera which is locked onto my player, and the camera has the ability to zoom in on the player using the scroll wheel with set limits for it, however I am trying to figure out how I can make the camera angle change smoothly depending on how far I am from the player.

Code (CSharp):

1. void LateUpdate ()
2.     {
3.         distance += Input.GetAxis("Mouse ScrollWheel");
4.         distance = Mathf.Clamp(distance, distanceMinMax.x, distanceMinMax.y);
5.  
6.         if (distance < 3)
7.         {
8.             // if the camera is closer than 3 units away change the y angle offset of the camera
9.             offset.y = 2;
10.         }
11.         else
12.         {
13.             offset.y = 5;
14.         }
15.  
16.         transform.position = target.position + offset * distance;
17.         transform.LookAt(target);
18.     }

This code here works, however the camera's angle changes instantly, but I would like it to change gradually between the two set values. I tried using Lerp, however I'm not sure how to use it in this particular context.
Please help. Also if anyone has advice on how I can smooth the zoom without changing the sensitivity of the input settings, I would be most gracious.

 

Please help. I posted this late at night and so many may not have seen it.

 

lerp the position and rotation...

change the last 2 lines to something like:

Code (csharp):

1.  
2. //tweak the 0.5 values to your liking, values closer to 0 are slower, values closer to 1 are fast
3. transform.position = Vector3.Lerp(transform.position, target.position + offset * distance, 0.5f);
4. transform.rotation = Quaternion.Slerp(transform.rotation, Quaternion.LookRotation(target.position - transform.position), 0.5f);
5.  

You can also scale your incrementing of 'distance' as well. Something like:

Code (csharp):

1. distance += Input.GetAxis("Mouse ScrollWheel") * speed; //where speed is some configurable value

Maybe even through Time.deltaTime in there, see what happens...

 

Both of those suggestions work very nicely, thank you. There is a slight smoothing effect on the camera now, where if my character moves, the camera trails slightly behind, but I don't mind it that much so it's all good. I changed the last line back to transform.LookAt(target), as it doesn't seem to make a difference.