Real World: Growth Models

Calculus Readiness · Axiom Academy

One deposit, one exponential function — and the three questions it answers for the rest of your financial life. You put 2,000 in an account earning 5% a year, compounded annually. That single sentence is a function — B(t) = 2000(1.05)^t — and here are the three moves you can make with it. Press Grow and let the balance climb year by year. Each year it's the last year times 1.05 — that compounding is exactly what bends the curve upward. That's B(t) = 2000(1.05)^t , live. Now flip the question: you have a goal in mind — how long until you reach it? Drag a target balance and read the years straight off the curve. That's the inverse: . Here's the decision a saver actually makes: chase a higher rate, or not? Drag the rate and watch the 10-year balance pull away from the 5% account — and the doubling time collapse. Same function, new base 1+r . One function, three moves: read it (where will I be?), solve it (when do I get there?), weigh it (what changes the outcome?). Anything that grows by a fixed percentage each step is this same exponential — compound interest , inflation , populations , a viral share count — and these three moves are all you ever do with it.

This is the written version of the interactive lesson above. See the full Calculus Readiness course.