Learning Goal
Part of: Analyze functions using different representations — 9 of 10 cluster items
Interpret exponential function properties
**HSF.IF.C.8.b**: Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)ᵗ, y = (0.97)ᵗ, y = (1.01)^(12t), y = (1.2)^(t/10), and classify them as representing exponential growth or decay.
Show moreShow less
HSF.IF.C.8.b: Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)ᵗ, y = (0.97)ᵗ, y = (1.01)^(12t), y = (1.2)^(t/10), and classify them as representing exponential growth or decay.
What you'll learn
- Identify the initial value and growth/decay factor in an exponential function y = a·bᵗ
- Determine the percent rate of change from the base: growth rate = b - 1 when b > 1, decay rate = 1 - b when 0 < b < 1
- Classify an exponential function as growth or decay based on the base b
- Rewrite exponential expressions using exponent properties to reveal different time-scale rates (annual → monthly, daily → yearly)
- Interpret compound expressions like y = (1.01)^(12t) as equivalent to y = (1.01¹²)ᵗ ≈ (1.1268)ᵗ, revealing the annual rate from a monthly rate
- Explain the real-world meaning of the parameters in exponential models, including initial value, growth/decay factor, and percent rate
Prerequisites
Slides
Interactive presentations perfect for visual learners • In development
Slides
In development
Not yet available • Check back soon!