Interpret exponential function properties

Start lessonBegins with Growth decay and time scales · Slides

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Lesson Plan · Guided Notes · Exit Ticket · Re-teach · Homework

Lesson Plan →Objectives, pacing and practice, built from this lesson's brief.
Guided Notes →One page your students fill in and keep.
Exit Ticket →Three items at the end of class. No student accounts.
Re-teach →After an exit ticket: who missed what, and what to do tomorrow.
Homework →Assign practice; it grades itself.

HSF.IF.C.8.b

**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.

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*b^t
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 = (1.01^1^2)^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

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