Matt David, head of communications at Juul, said the company’s mission was to eliminate combustible cigarettes and noted that more than 50 percent of smokers who try Juul successfully switch to e-cigarettes.

The company found success by making something boring into something cool. Vaping was once a dorky punch line. Juul’s sleek devices deliver potent — and highly addictive — hits of nicotine in trendy flavors like mango and cucumber. It sharply rose in popularity among teenagers, catching many parents, schools and investors by surprise.

“This is like one of those fires that raked through tens of thousands of acres overnight,” Mr. Burke, the investor at Makena Capital, said. In September the Food and Drug Administration called the popularity of vaping products an “epidemic,” and ordered Juul and other makers to prove that they could keep its devices from minors. A little over a week ago, the F.D.A. seized documents from Juul’s office in a move the agency described as a surprise inspection.

Mr. David said Juul had taken numerous actions to prevent and combat underage use of its product. It has changed its website and marketing to focus on smoking cessation, added a nicotine warning label and started an advertising campaign aimed at smokers. Tao Capital did not respond to a request for comment. Both Fidelity Investments and Tiger Global declined to comment.

Lucy Nicotine, a nicotine gum start-up, generated investor attention in March, when it participated in Y Combinator, a start-up accelerator program, because two of its founders were well-known for their prior start-up, Soylent, a meal replacement drink. Lucy raised just under $5 million in venture funding led by Greycroft Partners and Refactor Capital.

In early meetings with potential investors, the company’s presentation included a slide outlining the benefits of nicotine, like energy and alertness. But the company quickly stopped promoting that aspect.

Teddy Citrin, an investor at Greycroft Partners, said his firm was initially concerned about stigma and taboo of investing in a nicotine company, but was won over by the potential to help people quit smoking.