The number N of farms in the United States has declined continually since 1950. In 1950, there were 5.6 million farms, and in 2008 that number had decreased to 2.2 million (Sources: U.S. Department of Agriculture; National Agricultural Statistics Service)
Assuming that the number of farms decreased according to the exponential decay model:
a) Find the value of k, and write an exponential function that describes the number of farms, in millions, after time t, in years, where t is the number of years since 1950.
b) Estimate the number of farms in 2011 and in 2015.
c) At this decay rate, when will only 1,000,000 farms remain?