Over the past six years, Colorado has conducted one of the largest ever real-life experiments with long-acting birth control. If teenagers and poor women were offered free intrauterine devices and implants that prevent pregnancy for years, state officials asked, would those women choose them?

They did in a big way, and the results were startling. The birthrate for teenagers across the state plunged by 40 percent from 2009 to 2013, while their rate of abortions fell by 42 percent, according to the Colorado Department of Public Health and Environment. There was a similar decline in births for another group particularly vulnerable to unplanned pregnancies: unmarried women under 25 who have not finished high school.

“Our demographer came into my office with a chart and said, ‘Greta, look at this, we’ve never seen this before,’ ” said Greta Klingler, the family planning supervisor for the public health department. “The numbers were plummeting.”