A pile can grow two ways. ADD the same block every day and it climbs a straight ramp. DOUBLE it — pile a slice of itself on top — and it bends upward.
The steady way: drop another $1,000 on the pile every day. Every block is the same size, so it climbs a straight ramp — it never speeds up.
Meet the racers. Steady Sam adds $1,000 a day. Doubling Dot starts with one penny that doubles daily. After a week Sam has thousands — Dot still has pennies.
Now drive the penny. Drag the days and watch it double: 1¢, 2¢, 4¢, 8¢… each jump is bigger than the whole pile before it.
See how flat it starts, then the curve bends up? That bend is the secret.
Two weeks in, Sam's pile towers up. Dot's penny is still pocket change. It looks hopeless for the penny… but the race runs to day 30. 🤔
Sam adds a fixed $1,000 a day. Dot's penny doubles every day.
It's day 30. Who has more money?
Drag to day 30 — watch the gold penny 🏁