Slerping in movement speed?

I been reading a bit about slerping, and I’m not sure I can use it in my javascript, or exactly how it’s working for calculations. I’m using a script for camera movement, RTS, and when you move the camera to the defined boundries, it starts scrolling, at the speed of a given variable [scrollSpeed], but this feels jerky, it takes you to full speed instantly, and it’s hard to do precise movement. Is there a way to put like a function onit, so it starts out slow, and then builds in speed, til reaching the defined speed?

myVector = (Vector3(mySpeed,0,0) * scrollSpeed * Time.deltaTime);
using UnityEngine;
using System.Collections;
public class SmoothMover : MonoBehaviour
{
	//animation curve is nice for any y=f(x) to use in gameplay
	//use smooth function here. check it in inspector for graphic representation
	public AnimationCurve MoveSpeed = new AnimationCurve(new Keyframe[] 
	{ 
		new Keyframe(0.0f, 0.0f, 0.0f, 0.0f),
		new Keyframe(0.3f, 0.1f, 1.0f, 1.0f),
		new Keyframe(0.5f, 0.5f, 2.0f, 2.0f),
		new Keyframe(0.7f, 0.9f, 1.0f, 1.0f),
		new Keyframe(1.0f, 1.0f, 0.0f, 0.0f) 
	});
	//coordinates where we move from and to
	public Vector3 MoveFrom = Vector3.zero;
	public Vector3 MoveTo = Vector3.right * 10f;
	//object that we move
	Transform movingObj;
	void Start()
	{
		//simple create here a primitive to check how it works
		movingObj = GameObject.CreatePrimitive(PrimitiveType.Sphere).transform;
	}
	void Update()
	{
		//the main line of code 8)
		//Vector3.Lerp gives us a point between two points on needed offset in 0..1 range
		//MoveSpeed.Evaluate returns a y=f(x) from smooth function
		//Mathf.PingPong simple returns x that
		//changes in time from 0 to 1, then to 0, then to 1 etc
		movingObj.position = Vector3.Lerp(MoveFrom, MoveTo, MoveSpeed.Evaluate(Mathf.PingPong(Time.time * 0.5f, 1f)));
	}
}

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