Fill Experience Level Bar fast to slow

Hi, I made a level bar fill which goes from 0 to 1 for each level acquired. The value is a float. It increases with potions. I want the bar to go fast in the beginning and slower as it reaches it's target level/Exp.

The problem is that if I increase the level from 1 to 20 using Time.deltaTime. It goes towards the targeted level but at the same speed. I tried different Mathf as well. Some do the trick but since the value is a float, towards the end of reaching the targeted level is becomes REALLLY slow. Which is something I don't want.

Is there a way for me to control the speed depending on the experience bar reaching the targeted level? Thanks

Here's my code using Mathf.MoveTowards :

 ExperienceSlotUI[] expSlots;
 LevelWindow levelWindow;
 [SerializeField] public Button levelUpBtn;
 public Animation anim;
 [SerializeField] ParticleSystem particle;
 [SerializeField] ParticleSystem particle2;
 public int currentLevel;
 public int level;
 public float speed = 0.5f;
 public float XpToAdd;//For ExpSlotUI;
 private float target = 0;


     private void UpdateAddExperience()
     {
         
         if (levelWindow.expBarImage.value < target)
         {
             levelWindow.expBarImage.value = Mathf.MoveTowards(levelWindow.expBarImage.value, target, speed);
             
         }
         if (levelWindow.expBarImage.value >= 1)
         {
             IncreaseOriginalBar();
             ShowExperience(0);
         }
         if(levelWindow.expBarImage.value >= target)
         {
             isAnimating = false;
             //Restart XpToAdd
             XpToAdd = 0;
             //Faire disparraitre un mask transparent
             Destroy(mask);
             //activate btn
             EnableExpBtn();
             //Deactivate particle effect
             particle.Stop();
             particle2.Stop();
 
         }
     }
 
    private void LevelUP()
    {
         levelWindow.expBar2Image.gameObject.SetActive(false);
         levelWindow.expBarImage.gameObject.SetActive(true);
 
         ShowExperience(XpToAdd);
         //Faire apparaitre un mask transparent
         SetupMask();
         //Reset expUsed
         ResetExpUsed();
        
         
         
         //Add to baseStats
         levelWindow.baseStats.IncreaseXP2((int)(XpToAdd));
 
         //Deactivate levelup btn
         levelUpBtn.enabled = false;
     }
 
     private void ShowExperience(float expToAdd)
     {
         target = ((levelWindow.baseStats.GetPoints() + expToAdd) / levelWindow.baseStats.GetRequiredXPForLevel(currentLevel));
         isAnimating = true;
         
     }: