You are partially right in mentioning China and India. Backwards countries that become industrialized have not fit this model very well because a more efficient use of resources will affect the parameters. However China has instituted severe population control policies that are offsetting the industrialization of these two countries; they probably wash each other out, and the global population prediction is still valid.
Look, either your formula is accurate or it isn't. Either I am right or I am wrong. Either your faith in the forumula is justified or it isn't.
You lofted the forumula. I observed that it isn't accurate due to the examples given. You stated, "Yes but." Sorry, nice try.