The device in a network that keeps track of connected devices' MAC addresses is the:

A switch is the correct choice because it operates at the data link layer of the OSI model and is designed to manage the flow of data within a local area network. One of its primary functions is to maintain a MAC address table, which it uses to keep track of the MAC addresses of the devices connected to it. This capability allows the switch to intelligently forward data packets only to the specific device intended, rather than broadcasting the packets to all connected devices.

This selective forwarding boosts network efficiency and greatly reduces unnecessary traffic. In contrast, a hub performs a more simplistic function by broadcasting the incoming data to all connected devices without regard to their MAC addresses, which results in increased network collisions and inefficiencies. A router primarily directs traffic between different networks rather than managing MAC addresses, while a modem serves to convert and modulate digital data for transmission over phone lines or cable systems, lacking the functionality to track MAC addresses in a network.