mathematics – Predict future position of a moving body in Phaser’s arcade physics

I am looking for an equation for predicting the future position of a moving arcade physics body in Phaser 3. The body has drag applied and isDamping set to true. Phaser applies the drag using the following run on each update (showing x axis only but same applies to y).

//  Damping based deceleration
dragX = Math.pow(dragX, delta);

velocityX *= dragX;

Given the above, how would I write a kinetic equation to predict the future position?

I am currently using the method below, where I am iterating over frames to calculate the position accumulatively. But this is inefficient and inelegant so would prefer a solution which estimates the position without any looping.

public futurePosition(timeInSeconds: number): Phaser.Math.Vector2 {
  const DELTA = 1 / 60; // Assume we are running at 60fps
  const DRAG = 0.3; // Drag value
  const position = this.position.clone(); // Current position of body
  const velocity = this.body.velocity.clone(); // Current velocity

  // Inefficiently looping through frames
  for (let i = 0; i < timeInSeconds / (DELTA * 1000); i++) {
    velocity.x *= Math.pow(DRAG, DELTA);
    velocity.y *= Math.pow(DRAG, DELTA);
    position.x += velocity.x * DELTA;
    position.y += velocity.y * DELTA;

  return position;

Any help appreciated. Thanks.