Caryn Mathes, general manager of WDET 101.9 FM, will leave the public-radio station after February to take a position with another station serving the Washington area. Mathes has worked at WDET for 22 years, 20 of them as general manager. During her tenure, the Detroit-based station's support from individuals has increased nearly 500 percent, underwriting support has grown by $1 million, the station's weekly audience has increased 280 percent, and it has begun accepting Web-based donations. Mathes will stay on at the Wayne State University station through February to help with the transition and a national search for her successor.