Where would I put the slerp to smooth this out?

Where would I put the slerp in this line of code?

this.transform.Translate (0, 0, 0.85f);

Use the Vector3.Slerp like this

public float time = 0.85f;

this.transform.position = Vector3.Slerp(0, 0, time);

I hope this will work for you