More detailed data confirm the claim.

This chart is taken from https://ourworldindata.org/fossil-fuels ; most data there comes from the published paper:

*Vaclav Smil (2017). Energy Transitions: Global and National Perspectives. & BP Statistical Review of World Energy.*. 

It is coherent with figures from the World Bank: https://data.worldbank.org/indicator/EG.USE.COMM.FO.ZS ; https://data.worldbank.org/indicator/EG.USE.PCAP.KG.OE

[![fossil fuel consumption][1]][1]

The growth is indeed exponential or, arguably, linear since 1950 with a strong slope.
The consumption reached 83,000 TWh in 1990, then 134,000 TWh in 2017.

Using data from the same source, the aggregated numbers confirm that 50% of total (1800-2017) consumption of fossil fuel has happened after 1990.

*I basically summed the data in the online-available spreadsheet; I don't think that should be dismissed as "personal research" ?*

  [1]: https://i.stack.imgur.com/nHNj4.png