Study guides › Level 8 · Algebra 2

Doubling and halving over time

Level 8 · Algebra 2 · for questions like “50 bacteria double every 3 hours. How many after 12 hours?”

💡 The idea

Count how many doubling (or halving) times fit, then double (or halve) that many times.

amount = start × 2ⁿ (or start ÷ 2ⁿ)

✏️ Worked examples

1. 50 doubling every 3 hours, after 12 hours: that's 4 doublings, so 50 × 16 = 800.

2. 400 mg halving every 6 days, after 18 days: that's 3 halvings, so 400 ÷ 8 = 50 mg.

⚠️ Watch out

• It's not 4 × 2 = 8 times bigger. It's 2 × 2 × 2 × 2 = 16 times.

🎯 Try these

1. 30 doubling every 2 hours, after 10 hours
2. 640 halving every 5 days, after 20 days
3. 100 doubling every 4 hours, after 12 hours

Answers: 1) 960 2) 40 3) 800

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