I answered on the facts of this question already on skeptics.SE, here and here. You should read both papers very carefully, I highlighted the most important facts but this is a very tricky question, esp. when it comes to defining what mental activitiy is. The papers also give an explanation of how fMRI signal is linked to NEURONAL activity, as far as I remember there is no strong direct link.
You assume in your question that a mathematician solving a differential equation needs higher mental activity than a child reading a book. Is this legitimate? It seems intuitive but also very subjective. In the paper they mention that for the highest and lowest energy consumption we lose consciousness. I will not draw conclusions from this. However, you are talking about conscious mental activities so this may answer your question. To me it means more that the understanding of the human brain in neurobiololgy is on the level of the Rutherford Atomic Model in Physics at the beginning of the 20th century. We have not really got a clue how information is processed and how it's constrained by physical laws and principles of entropy and energy. By reading the 2 papers it looks more like the human brain is not raising energy consumption as a computer would (the computer analogy pretty much fails when compared to the human brain). Most of the energy is used for unconscious processes in "standby mode".
As in physics, extreme cases such as savants and the mentally disabled are probably the best starting point to exclude possible models of human brain and physical boundary conditions as we cannot approach the questions of human brain in a reductionistic way. How can savants like Kim Peek process such huge amounts of information AND save it. He is able to scan books pages just once and know them by heart thereafter. His brain does not, however, consume more energy than an average human brain. So mental activity is probably not a very good term, quantity, or even really suited to be scientifically used. Does neuronal activity mean mental activity (in the sense of your definition?) Reading the papers, the problem is the separation of mental and neuronal activities. At first you have to know what are the basic brain functions and processes that are consuming most of the energy. However the brain is not built in modular way like a computer (most energy is used here for constantly refreshing RAM). So there is not really a objective way to analyse and separate this modular energy consumption, if it even is modular.
In my opinion, most models about information processing in human brain are intuitive guessing (again Rutherford). We need much more detailed experiments and data (Blue Brain Project). fMRi is like analysing a atom with a magnifying glass. Also, the more prosperous approach from a biophysical perspective is probably not the level of "mental activity" but the hard-based amount of information processed by human brains and linked energy consumption (Kim Peek). But therefore we need a model of how this information is saved in human brain. Do normal humans save the same information as Kim Peek scanning a page or are we just unable to recall it consciouscly? When solving a differential equation, how much energy do you consume when recalling facts and is that experience not similar to reading a book? How much is mental logical tasks and is there really a difference at all?
I will stop here, hope you gained some insight that the question is of course important but too early to be definitively answered. I think we will learn a lot more from projects like Blue Brain as we have from fMRI experiments.