Updating tab badge dynamically on Ionic 2

I wish to update dynamically a badge value, when I click on a button.

tabs.html

...
        <ion-tab [root]="tab1Root" tabTitle="Product" tabIcon="search"></ion-tab>
        <ion-tab [root]="tab2Root" tabTitle="Cart" tabIcon="cart" tabBadge="{{cartCount}}" tabBadgeStyle="danger"></ion-tab>
...

tabs.ts

export class TabsPage {
...
    cartCount = 0;

    tab1Root = ProductPage;
    tab2Root = CartPage;
...
}

product.html

<button ion-button full (click)="updateCart('add', p.id)">Buy Now</button>

product.ts

export class ProductPage {
...
    updateCart(action, id) {
        let cartCount = 1;

        let alert = this.alertCtrl.create({
            title: 'Success!',
            subTitle: 'You have added 1 product to the cart.',
            buttons: ['OK']
        });

        alert.present();
    }
...
}

As I tought, let cartCount = 1; does nothing. I've searched for a solution, but most of them are for Ionic 1 or AngularJS, which didn't helped me at all.