One of the commenters offered a retort that I've seen in a bunch of places: "Of course Medicare is growing faster! It cares for a sicker population!"
It's a common intuition, but it's wrong. Consider a simple model of a population with two groups: young and old. Assume that the old consume five times as much of an undifferentiated good, healthcare, as the young do, and that each unit costs $2,000. So the oung cost us $2,000 apiece per year, and the old cost us $10K. Now assume that the cost of healthcare in each group grows at 10% a year. At the end of five years, each young person will cost us $3,221 and each old person will cost us $16,105--or exactly five times as much as a young person.
In other words, the fact that old people consume more healthcare than young people explains why the absolute difference in dollar amount of spending gets bigger over time. But it doesn't explain why the rates of growth differ.
Now, obviously "healthcare" is not a homogenous good. So there are a bunch of different reasons that healthcare spending growth rates might differ. We might get better at treating things that disproportionately happen to the elderly, causing the amount of healthcare they consume relative to the young to rise. The cost of treating things that the elderly disproportionately get might rise, causing the cost of their healthcare to rise relative to the young. They might succeed in using political power to divert more treatment resources to themselves. You can imagine a bunch of different factors.