This chart from the Federal Reserve Bank of St. Louis, shows the supply of U.S. currency over time.
From the beginning of the chart (1918) through about 1968, the rate of inflation Y/Y is low. Following 1972ish, the rate of inflation goes up very rapidly Y/Y and the money supply skyrockets. Even ignoring the post 1997 portions of this chart, which are outside the scope of this subreddit, the Fed seems to have had a policy of massively increasing inflation and the rate thereof through the 30-year period between 1968 and 1998. Why? Or am I misreading this?
This chart doesn't equate to rates of inflation, it measures the money supply in absolute terms.
Firstly; it measures the money supply in linear terms, but inflation is geometric. A steady 2% yearly inflation yields steadily growing yearly increases: 100->102->104.04 and so on. This gives an exponential curve on a linear graph such as yours.
Secondly: The money supply is a reflection of the total amount of goods in a system. As the economy grows the total value of everything in it grows too and more physical money is needed to allow trade among people. This doesn't affect the purchasing power of the money in your hand at all.
This is not too say inflation doesn't happen. Increases in the cost of linchpin goods such as gasoline, such as happened during the OPEC crisis, can increase the cost of practically everything and this shows up as inflation on most metrics used to track it. The government does use the money supply to try to control inflation, typically around 2.5% annually. The consistency is essentially to lower the risk to speculators to encourage investment in the economy and the positive figure is a stealth tax on liquid capital, again designed to encourage people to invest in the economy. We live in a capitalist system (society is organised around the needs of the money), so capital mobilization efforts like this are one of the most important activities of government.