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Index Laws in Science
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Index Laws in Science
🔬 Part 1: Daily Review - Index Laws Basics
1. Simplify (3⁴ × 3⁻²)²
2. Express 4⁵/4³ using index laws
3. Which scientific contexts use exponential growth or decay? (Circle all that apply)
Radioactive decay
Population growth
Sound intensity
Temperature measurement
☢️ Part 2: Half-Life Applications
4. A radioactive isotope has a half-life of 8 hours. Starting with 120 grams, how much remains after 24 hours?
Formula: Q = Q₀ × (1/2)ⁿ where n = number of half-lives
5. Error Analysis: Sam calculated that after 3 half-lives, 80g becomes 80 × (1/2)³ = 80 × 1/8 = 80/8 = 40g. What is Sam's error?
6. Simplify the expression (1/2)⁶ × 2³ using index laws
🔊 Part 3: Sound Intensity and Real-World Problem Solving
7. Sound intensity follows I ∝ 1/r² where r is distance. If intensity at 2m is I₀, what is the intensity at 8m?
I₀/4
I₀/16
I₀/8
I₀/2
8. Challenge Problem: A carbon-14 sample has a half-life of 5,730 years. Aboriginal rock art was tested and found to have 1/8 of the original carbon-14. How old is the artwork?
9. Extension: If sound intensity decreases from 80 dB at 3m to 20 dB at distance d, express d in terms of powers. Show your working using index laws.
10. Reflection: How do index laws help you understand scientific concepts like radioactive decay?
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