The mathematics of proportional change. Exponential functions model growth and decay; logarithmic functions are their inverses. Master sequences, the form ab^x, composition and inverses, logarithm properties, and how to solve equations and build models with both.
Six ways to master Unit 2 — pick whichever fits how you like to study.
All 15 topics from the College Board CED, in order.
Unit 2 is about proportional change — situations where a quantity grows or shrinks by a constant factor rather than a constant amount. It opens by contrasting arithmetic and geometric sequences (and their linear and exponential cousins), then develops exponential functions of the form f(x) = ab^x, including growth versus decay, the horizontal asymptote, and how to build and validate exponential models from data.
The second half introduces the exponential function's mirror image. Through composition and inverse functions, you meet the logarithm — the inverse of the exponential — and learn its graph, its domain and vertical asymptote, and the product, quotient, power, and change-of-base properties. These tools let you solve exponential and logarithmic equations, build logarithmic models (pH, decibels, earthquake magnitude), and read semi-log plots, where exponential data appears as a straight line.
This unit is 27–40% of the exam and takes about 30–45 class periods. The three mathematical practices below run through every topic: