Rule of 70
The rule of 70 is a useful rule of thumb for quickly calculating the doubling time for something (e.g. population, GDP, internet nodes) that is growing at a constant rate; it says the doubling time is 70/growth rate. See the video for details and some examples.
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It would have been nice if you could include a quick mathematical basis for this. ie basically the rule of 70 is just because Log (2) = 0.69
I think question 3 is wrong: it asks for the rule of 70 given *4*% interest. 70 / 4 is 17.5 years which is not one of the options; the only answer which is accepted as right is the 35 year answer... but 35 is only the answer if you go 70 / 2%, and the question specifies explicitly 4%.
Why does it have to be a problem that 1/3 of GDP would be devoted to medical care? If rates continue to be like that, it means that in 35 years, population would also have double income, if 1/3 is then spent in medical care, that means that in the future, 2/3 of a doubled income is spent in everything else, that still is 60% more than 35 years ago. I wouldn't say that is a bad thing for anybody, really.
On the other hand, in a free economy, the amount of resources devoted to a particular expenditure depend on the free choices made by the people. If people are willing to spend 33% of their income in medical care, it is because they value it more than say automobiles or burritos. How can that be a problem?
Maybe is not a "problem" but probably a bad allocation of resources who bring to a massive failure of welfare states. It is like a vicious circle: people think than with modern and more expensives treatments the will defeat diseases (and death), so they live in an unhealthy lifestyle (lots of work, stress, bad food, etc.), then doctors and insurance companies raise the bet, tariffs go to sky, politicians offer "good health" to everybody (as if this was possible, the can only offer more expensive treatments), and so a bubble is created up to reach to a whole system broke
How much of the 4% of growth for medical expenses is due a bubble provoked by inefficient insurance systems, over demand of hypochondriacs, patents of big pharma, litigations and so on? Maybe at a certain point people and government simply will can´t afford the inflated expenses and will come back to take care more of their health by their-selves and accept that all we have to die someday, probably much of this huge growth is due the fat-cats syndrome on people convinced that good health is just matter of spend enough money in medical services