That said, I would suggest approaching this problem a little differently if you want to do it the more "Laravel" way.

It's certainly possible to make a system that would update DB values on access, but I would recommend against it. If you start showing the price in multiple views, you will have to make sure you are always running the same update function in every view. It's also very easy for a mistake to wreak havoc (if you accidentally run an update at a wrong interval it's hard to determine how you changed values, and you could easily modify a lot).

Instead I'd recommend using dynamic attributes on your Eloquent models. price has such a regular formula, it really doesn't need to be in the database at all, and other values, like the date of the next price change and whether the product is expired, can also be determined automatically in the model instead of the controller:

class Product extends Model {
  /* (your existing eloquent model code...) */

  // This special array will automatically mutate your date columns into
  // Carbon date objects, so you don't have to call Carbon::parse all the time
  protected $dates = ['created_at', 'start_date', 'expires_at'];

  // This is a custom accessor. It will run every time we try to
  // get $product->price. https://laravel.com/docs/5.2/eloquent-mutators
  public function getPriceAttribute()
  {
    // find the number of days since start_date, capped to a max of 9 days
    $daysSinceStart = min($this->start_date->diffInDays(), 9);
    // reduce the price by 10% every day
    return $this->msrp * (1-($daysSinceStart / 10));
    // (note that I leave the formatting to the front-end)
  }

  // This accessor returns the datetime of the next price change for use in a countdown timer.
  public function getNextPriceChangeAttribute()
  {
    $daysSinceStart = $this->start_date->diffInDays();
    return $this->start_date->copy()->addDays($daysSinceStart + 1);
  }

  // This accessor provides a boolean identifying whether 10 days have passed since the start.
  public function getIsExpiredAttribute()
  {
    return $this->start_date->diffInDays() >= 10;
  }

  // This special array lists attributes that are added to product listings
  // even when they don't exist in the underlying database. (the value is
  // determined using our accessor method above)
  protected $appends = ['price', 'next_price_change', 'is_expired'];

}

Then you can just use $product->price, $product->next_price_change, $product->is_expired in your controllers and views without having to make updates or calculate them each time.