A suspension cable of a bridge hangs in the shape of a parabola, modeled by the function $c(x)$, representing the height of the cable in meters above the bridge deck, $x$ meters horizontally from the center of the bridge. The lowest point of the cable is $10$ meters above the deck at the center of the bridge ($x=0$). The cable is attached to towers $300$ meters apart, and the height of the cable at the towers is $100$ meters above the deck. Based on this model, what is the estimated height of the cable above the deck, in meters, at a point $50$ meters horizontally from the center of the bridge?