How To Lerp With Acceleration

Hi all! Struggling with a problem and hoped I could get some help.

The main goal is sort of like a magnetic effect where theres an object pulling a bunch of smaller objects to it over time.
It was fairly easy to just get the basic lerp in a Co-Routine but figuring out the bit where it looks like its being accelerated into the centre over the same time has me a little lost.

Here’s the Co Routine I have. Any help would be greatly appreciated!

private IEnumerator RunMagnetizationCo(float posX, float posY)
{
    float duration = 1.5f;
    var t = 0f;
    var start = transform.position;
    var target = new Vector3(posX, posY, transform.position.z);

    while (t < 1)
    {
        t += Time.deltaTime / duration;

        if (t > 1) t = 1;

        transform.position = Vector3.Lerp(start, target, t);

        yield return null;
    }


    yield return null;
}

It’s probably possible using “Mathf.SmoothStep”, but I prefer using AnimationCurve.

//adjust this curve on the inspector
public AnimationCurve curve;

//------------------------------------------------------------------------
float t1 = curve.Evaluate(t);//insert to line 13
transform.position = Vector3.Lerp(start, target, t1);//replace t to t1 in line 14