For most of human history, the rate of growth could have been described by a simple hyperbolic function, that is because we have a feedback cycle of population causing more technology, which causes more population (having more inhabitable space, better food growth etc), which causes more technology. This function doubled the population in incrementally smaller frames of time, and if extended to the future, it would reach infinity in a finite amount of time.
A science paper published by Heinz Von Foerster in the 1950s shows that the hyperbolic function that humanity followed up until the time of that paper, is going to reach infinity on November 13, 2026.
Unfortunately, humanity would break out of that pattern just 10 years later, because population stopped growing hyperbolically (at least in developed countries, which were the only ones really affecting the technology and economy in a meaningful way).
fun fact: the industrial revolution doesn't show on this graph, because on the larger scale, it was natural for technology to 'boom' around that time
on this graph it looks like there's been a revolution, but its the same graph as the one above, a hyperbolic function, if you transformed it to a log doubling time graph it would look like a straight line
Is the singularity still possible
Yes, the reason we broke off the pattern is because more technology ➜ more food ➜ more population ➜ more technology, and we decided to just not grow population like we used to, but that pattern can change.
So far technology couldn't make more technology on its own, we needed it to afford more humans, but eventually we will have advanced AI, who will transform the pattern into technology ➜ better AI ➜ more technology, removing human growth from the equation.