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More detailed data confirm the claim:

This chart is taken from https://ourworldindata.org/fossil-fuels

fossil fuel consumption

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

I will look for aggreagated numbers to confirm if 50% of total consumption has happened since 1990, but visually it seems correct.