As a starting point, remember that the number of elderly in the U.S. population is rising: the number of Americans age 65 and over will more than double from 2010 to 2050; the number of Americans 80 and over will nearly triple; and the number of American 90 and over will quadruple.
It's already true, as one might expect, that older Americans typically have higher health care costs paid by Medicare. (One caveat: The results that follow are based on data from "traditional" Medicare, in which the governmment reimburses service providers as services are paid, and thus don't include the 25% of Medicare Advantage recipients, a program where the government pays the health care provider a fixed amount each month. Of course, the hope of a fixed payment or capitated health care plan is that it gives the provider an incentive to find ways of holding down costs.) For example, those 80 and older are 24% of those receiving traditional Medicare, but receive 33% of Medicare spending.
A more detailed breakdown of per capita Medicare spending by age shows a steady rise with age, although this peaks out around age 95, and also offers a more detailed sense of which expenditures are rising and falling with age. The data also allows separating out the health care costs of those who died in a specific year, which offers at least a rough way of looking at the extent to which end-of-life health care costs are influencing these spending patterns. Thus, the blue line shows per capita payments from traditional Medicare by age in 2011. The orange line, slightly lower, leaves out those who died in 2011. Notice that both lines rise, although the blue line rises more sharply, which suggests that end-of-life costs play a role in the higher costs by age, but are by no means the main factor.
Trends in End-of-Life Care" (February 25, 2013), which found that about 25% of Medicare payments are for those in their last year of life. But in addition, it's interesting that the amount spent in last year of life is highest at about age 70, and falls after that point. The implication would seem to be that more extreme health care spending efforts are being made to assist the "younger old" at around age 70 than the "older old" in their 90s and beyond.
The use of hospice care also seems to have increased substantially in the last decade or so. On a per person basis, about $550 was spent for hospice care for 100 year-olds in 2000; in 2011, about $3,049 was spent on hospice care for 100 year-olds.