Read the Application: Health Care Spending
Exponential growth functions increase at an increasing rate. We can observe this by calculating the average rate of change on different intervals of the function. [You may want to refer to Section 2.4 to review average rate of change].
The graph models healthcare spending by the U.S. Government.
Estimating from the graph, it would appear the y-value is 1580 in 2016, 790 in 2006, and 400 in 1996.
We first calculate the slope of the straight line that would connect the points (1996,400) and (2006,790).
(790 – 400)/(2006 – 1996) = 390/10 = 39 billion dollars per year.
Now the slope of the straight line that would connect the points (2016,1580) and (2006,790).
(1580 – 790)/(2016 – 2006) = 790/10 = 79 billion dollars per year.
These are average annual rates of change. The average annual increase in health care expense went from $39 billion per year on the interval (1996,2006) to $79 billion per year on the interval (2006,2016). The rate of increase doubled.