Lesson Plan

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

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.