KAHULUI, Hawaii — It had been 17 days since anyone had seen Amanda Eller. Her car was spotted near a trailhead in a vast forest reserve in Hawaii, and thousands of search volunteers were scouring the jungles and streams nearby. On Friday afternoon, less than an hour after her family announced a $50,000 reward for information, rescuers found Ms. Eller with a broken leg, sunburns and scrapes, and a torn meniscus in her knee.

She was malnourished and dirty. But alive.

“I wanted to give up,” Ms. Eller, 35, said from her hospital bed late Friday night. “But the only option I had was life or death.”

Ms. Eller, a physical therapist and yoga instructor, said she lost her way in the Makawao Forest Reserve on the northern side of Maui on May 8, turning a three-mile hike into a two-week fight for her life.