The best guess is that there are 3,000 to 4,000 goats in the state, down from an estimated 9,000 in 1960.
Rice doesn't know how many goats remain in the Darrington area, but said the Snohomish County group makes up one of the state's most struggling populations.
Four years ago, the Sauk-Suiattle Tribe, which views the goat as a sacred part of its cultural heritage, pressed to get wildlife biologists to start looking into what was behind the species' mysterious decline.
Now state biologists are in the second year of a four-year study to map out where the goats go in the summer and - the bigger unknown - in the winter.
The Fish and Wildlife Department is spending $150,000 a year to collar and track goats up and down the Cascades. The Sauk-Suiattle Tribe contributed $250,000 in grant money to help pay for the study.
So far, 40 animals have been outfitted with collars that use Global Positioning System technology, which maps their location every three minutes.
The information will help land managers better regulate hunting, recreation and logging, all of which could be harming the goats, said Phyllis Reed, a biologist with the Mount Baker-Snoqualmie National Forest.
The hunting of goats is widely thought to be the main reason goat populations have fallen.
Biologists once assumed that goats would rebound from hunting like deer, which produce more offspring when overhunted. But goats don't bounce back as quickly.
Their populations do recover, and biologists say they could rebound now that hunting is mostly banned throughout the Cascades, including in Snohomish County.
In the mid-1990s, the state cut back the number of goat hunting permits it issued to just 20 a year. And those goats can only be taken from populations that are thriving, Rice said.
Because of past hunting, goats remain wary of people, which means hikers and rock climbers could be keeping goats away from their prime feeding areas. Reed said snowmobile use in the winter may also keep goats from the best feeding areas and from shelter.
Norma Joseph, a member of the Sauk-Suiattle's cultural committee, spoke of a time when mountain goats were so abundant, "you could go outside your back door and see them."
"We used to make elaborate blankets and clothing that we would trade with other tribes," she said. "That's a resource that's gone to me."