Question: The American rock band whose guitarist Nuno Bettencourt went on to lead the band Mourning Widows, whose second album was Furnished Souls for Rent, reached the height of its popularity in what decades?

Context paragraphs:
Love (DramaGods album): Love is an album from DramaGods, a project led by guitarist Nuno Bettencourt.  Bettencourt is most remembered for being the guitarist in the band Extreme.  Originally conceived as a double-album entitled "Love/Hate", the songs were combined into one album.  It is not known what happened to the rest of the songs from these recording sessions, if they were ever fully recorded and produced, or just left as demos.

Sessions from Room 4: Sessions From Room 4 is an EP released by the band Population 1, led by ex-Extreme/DramaGods guitarist Nuno Bettencourt.  The EP is the first official release from the band Population 1, which was previously just a solo project by Nuno Bettencourt.  They had to change the name of the band, not once, but twice due to legal reasons.  They were briefly known as Near Death Experience (a name Bettencourt had floated before for previous projects) and subsequently DramaGods, under which they released their next and only album to date, "Love".  "Sessions From Room 4" was released through the band's official website, and came with stickers and a limited edition autographed poster of the band.

Population 1 (album): Population 1 is the debut album of the project of the same name.  The project is led by Nuno Bettencourt, formerly of Extreme.  Some of the songs feature former Mourning Widows bandmates Donovan Bettencourt (bass) and Jeff Consi (drums).

Nuno Bettencourt: Nuno Duarte Gil Mendes Bettencourt (born September 20, 1966) is a Portuguese-American guitarist, singer-songwriter, and record producer.  He is best known as the lead guitarist of the Boston rock band Extreme.  He has also recorded a solo album as well as having founded bands including Mourning Widows, Population 1, DramaGods, The Satellite Party (headed by Jane's Addiction's then-former frontman and Lollapalooza co-founder Perry Farrell).  In 2007 he also reunited with Extreme to record new music and tour, with the band planning to release material sometime in 2017.

DramaGods: Dramagods (formerly known as Population 1) is a rock band led by Extreme guitarist Nuno Bettencourt.

Mourning Widows: Mourning Widows was a musical project led by former Extreme guitarist Nuno Bettencourt.  The band was formed in 1997, and they released two albums during their career.  Despite not being widely released in the United States, both albums were successful in Japan.  Bettencourt formed the band after the moderate success of his 1996 solo album, Schizophonic.  The band's sound went back to a funkier guitar-driven rock reminiscent of Extreme, while still having post-grunge and alternative influences.

Schizophonic (Nuno Bettencourt album): Schizophonic is the 1997 debut solo album from guitarist Nuno Bettencourt, the lead guitarist in the band Extreme.  Bettencourt is credited on the cover simply as "Nuno".  "Schizophonic" is Bettencourt's first and, so far, only solo effort after the group disbanded.

Furnished Souls for Rent: Furnished Souls for Rent is the second album released by Mourning Widows, a band led by former Extreme guitarist Nuno Bettencourt.

Extreme (band): Extreme is an American rock band, headed by frontmen Gary Cherone and Nuno Bettencourt, that reached the height of their popularity in the late 1980s and early 1990s.

Mourning Widows (album): Mourning Widows is an album by Mourning Widows, a project led by former Extreme guitarist Nuno Bettencourt.  The album was first released by Polydor Records in Japan and later in the United States.

Supporting paragraphs: Furnished Souls for Rent Extreme (band)
Answer: late 1980s and early 1990s