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.
Your Deliverables:
1. Post a graph of an exponential growth model. Show that it is
increasing at an increasing rate by calculating the average rate of change on
two different intervals. [You can follow the procedure used on the health care
spending application.]
Some good places to look for exponential growth graphs: sites
dealing with medical costs, government expenditures & debt, population
models, pension indebtedness, energy usage, computer memory & processor
speed. Don’t forget to cite your source.
2. What are the key takeaways you have from this chapter –
Exponential and Logarithmic Functions?
3. Are any topic/s in this chapter that you struggle with?
Please share them here, and be very specific.