Exponential functions

The Most Important Equation

Exponential functions through the lens of compounding — one of the most useful ideas in mathematics.

1
Hookvideo

One Dollar, One Hundred Years

A single dollar at 7% annual interest becomes $867.72 in 100 years. Not because 7% adds up — but because interest earns interest. The video makes the surprise land before explaining why.

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2
Exploration

Building the Formula Yourself

Students fill in a compound interest table year by year, discovering the pattern of repeated multiplication before the formula A = P(1 + r)^t is introduced.

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3
Explanationvideo

A = P(1 + r)^t

Deriving the compound interest formula from the table, naming each variable, then applying it: $5,000 invested at 18 vs. 28, and a $2,000 credit card balance at 20% over 10 years.

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4
Application

The Equation at Work

Four problems: an inherited $3,000, a credit card spiral, working backwards from a savings goal using P = A / (1 + r)^t, and the counterintuitive story of two investors who start at different ages.

Work through problems
5
Discussion

Why Isn't This Taught Earlier?

Who benefits from people not understanding compound interest? Students look up the gap between typical credit card rates and savings account rates and consider what it reveals.

Go to discussion
6
Capstone

Your Financial Timeline

Choose a financial goal, run the numbers forward and backward, and write a reflection on what the formula changes about how you think about money.

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Where this shows up

Compound interest, investment growth, debt accumulation