"every natural population experiencing exponential growth over the long term collapses. And even drastic measures like reducing the population by half only buys

"every natural population experiencing exponential growth over the long term collapses. And even drastic measures like reducing the population by half only buys you one 'doubling time'" But if you halve the population, you aren't experiencing exponential growth. Are we even experiencing exponential growth now, I thought we had passed peak child? Plus people have been making claims that we cant feed X billion people for the last 70 years, is there any particular reason why your prediction will be correct, where all others weren't?