DWG NO. 03 — Unit 3 of 10
6 online lessons · 1 in-person Review & Practice Day
Every function so far has grown by adding — a polynomial's output changes by a fixed amount, or a fixed multiple of x, for each step. An exponential function grows by multiplying: the same growth factor applies again and again, and the effect compounds. That single shift in how growth works produces a curve unlike anything in the last two units, and unlocks the mathematics behind compound interest, population growth, and radioactive decay.
The second half of the unit turns exponentials inside out. A logarithm is the inverse of an exponential function — a callback to inverse functions from 1.6 — and once you can move fluently between exponential and logarithmic form, a whole family of equations that looked unsolvable become routine.
Exponential Functions and Their Graphs
The form f(x) = a·\(b^{x}\), and how the base b controls growth, decay, and shape.
→The Number e and Exponential Growth/Decay
Where e comes from, and the continuous growth/decay model A = \(A_{0} e^{kt}\).
→Logarithmic Functions as Inverses of Exponentials
Converting between exponential and logarithmic form, and graphing log functions by reflecting across y = x.
→Properties of Logarithms
The product, quotient, and power rules, plus the change-of-base formula.
→Solving Exponential and Logarithmic Equations
Isolating the variable when it's stuck in an exponent or inside a log.
→Applications
Compound interest, half-life, and logistic growth — exponential models with a ceiling.
→Review & Practice Day 3 — bring your questions from lessons 3.1–3.6. You'll work practice problems, get feedback, and take the Unit 3 test.