The Pandemic That Taught Us Exponentials
The Pandemic That Taught Us Exponentials
In March 2020, a single person infected with COVID-19 in a small town became 2 people the next week, then 4, then 8, then 16. By week 10, if left unchecked, that single case would have become over 1000 infected people - this is the terrifying power of exponential growth. But nature also shows us the beauty of exponentials: bacteria doubling every 20 minutes to help break down waste, radioactive carbon-14 atoms decaying at a predictable rate that lets archaeologists date ancient artifacts, and compound interest in your bank account growing your savings faster than you might expect. From the spread of viral videos on social media to the cooling of your morning coffee, exponential growth and decay are the mathematical heartbeat of change in our world.
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Exam Success Strategies
- Identify growth vs decay first: Look for keywords like "increases", "doubles", "grows" vs "decreases", "halves", "decays"
- Convert percentages carefully: 5% increase means multiply by 1.05, not 0.05
- Count time periods correctly: If something doubles every 2 hours over 8 hours, that's 4 periods, not 8
- Use special formulas for doubling/halving: N₀ × 2ⁿ for doubling, N₀ × (0.5)ⁿ for halving
- Check reasonableness: Growth should give bigger values, decay should give smaller values
- Round appropriately: Money to 2 dp, bacteria to whole numbers, percentages to 1 dp
- Watch units: Time periods must match the rate period (yearly rate needs years, not months)
Now try it yourself
Quiz · Question 1 of 12
A quantity increases by 8% each year. Which multiplier should be used for each year?
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This topic in real past papers
Every real exam question we've found on growth & decay, with a full worked answer.