Recognize constant percent rate situations

What you'll learn

1. Define "constant percent rate" as a fixed percentage of the current value added or subtracted each period, and connect this to the base of an exponential function
2. Identify constant percent rate situations from verbal descriptions by recognizing key phrases such as "increases by 5%," "depreciates 12% per year," "doubles," "halves," and "grows by a factor of"
3. Convert a percent rate to a growth factor (1 + r for growth, 1 - r for decay) and write the corresponding exponential function
4. Distinguish constant percent rate situations (exponential) from constant rate situations (linear) in verbal descriptions
5. Explain why constant percent rate produces exponential behavior: each period, the AMOUNT of change is proportional to the current value, so larger values produce larger changes
6. Write and interpret exponential functions g(x) = a * b^x from constant percent rate descriptions, identifying a as the initial value and b as the growth/decay factor

Prerequisites

• Prove growth properties of functions