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Growth: Exponents and Logs

Watch doubling explode, run it backwards with half-life and count doublings with logs.

Intermediate · 11 lessons · Free, no account needed

Best after: Algebra in Motion

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Lessons

1. Doubling Is Wild (5 min): Doubling again and again is a power: after n folds the stack is 0.1 mm × 2ⁿ.
2. Exponent Rules by Counting (7 min): Multiplying powers of the same base joins the rows: 2ᵃ · 2ᵇ = 2ᵃ⁺ᵇ.
3. Shrinking: Zero and Negative Powers (7 min): Each floor down divides by the base, so 2⁰ = 1: it is just the next floor after 2¹ = 2.
4. Half Steps: Roots as Powers (7 min): A half step of doubling multiplies by the number that, done twice, gives 2: 2^(1/2) = √2 ≈ 1.414.
5. Growth Curves and Percent Growth (7 min): An exponential function is y = a · bˣ: start at a, multiply by b every step.
6. Half-Life: Growth in Reverse (7 min): Exponential decay multiplies by the same factor below 1 every step, so the amount keeps halving.
7. Logs Count Doublings (7 min): A logarithm counts doublings: log₂ 1024 = 10 because 2¹⁰ = 1024.
8. Log Rules: Exponent Rules Backwards (7 min): log₂ x is the inverse of 2ˣ: its graph is 2ˣ reflected in y = x.
9. Log Scales (7 min): On a log scale, each equal step multiplies by the same number, usually 10.
10. Faster and Faster: the Number e (7 min): Compound interest pays interest on interest: 50% twice turns $1 into $2.25, not $2.
11. Project: Will It Go Viral? (8 min): An exponential fits the first days of a viral video, then overshoots: the audience runs out.

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