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].

 

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.

 

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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.