CurveGrowUp.cs

using System.Collections;
using UnityEngine;

public class CurveGrowUp : MonoBehaviour
{
    Coroutine coroutine;
    //First keyframe of the animation
    public Vector3 startScale;
    //Last keyframe of the animation
    public Vector3 endScale;
    //Animation duration
    public float animationTime = 2f;
    //Animation curve 
    public AnimationCurve curve;

    private void Update()
    {
        if (Input.GetKeyDown(KeyCode.Space))
        {
            if (coroutine != null)
                StopCoroutine(coroutine);

            coroutine = StartCoroutine(IEScale());
        }
    }

    private IEnumerator IEScale()
    {
        float t = 0;
        do
        {
            //Calculation the current time percentage in a 0 to 1 scale
            float percent = t / animationTime;
            //Using that percent to find a correspondent value in our curve
            float curveValue = curve.Evaluate(percent);
            //Using the value of the curve (0 to 1) in our lerp
            transform.localScale = Vector3.Lerp(startScale, endScale, curveValue);

            t += Time.deltaTime;
            //Wait the next frame to run the next loop
            yield return null;
        } while (t <= animationTime);
    }
}