php - Carbon date formatting instance for laravel 8.12

one text

I have an array that is supposed to return the following date time:

$end_at = Carbon::now()->$toexpire($digit)->toDateTimeString();

but after upgrading from laravel 7 to 8.12, i get this error when i sign up for a plan from my website dashboard

TypeError Carbon\Carbon::singularUnit(): Argument #1 ($unit) must be of type string, null given, called in /home/legitmet/public_html/vendor/nesbot/carbon/src/Carbon/Traits/Units.php on line 239

this is the full function

public function joinPlan(){
    sleep(2);
    $this->feedback = 'Please wait';
    //get user
    $user=User::where('id',Auth::user()->id)->first();
    //get plan
    $plan=Plans::where('id',$this->planSelected->id)->first();
    // setup
    $expiration = explode(" ", $plan->expiration);
    $digit = $expiration[0];
    $frame = $expiration[1];
    $toexpire =  "add". $frame;
    $end_at = Carbon::now()->$toexpire($digit)->toDateTimeString();