Advanced MathVery hardYearly percentage from a doubled exponent
Advanced Math practice question
The function P(t) = 500(1.04)^(2t) models a population t years after 2020. By what percentage does the population increase each year?
Answer: 8.16
Each year the multiplier is (1.04)² = 1.0816, an increase of 8.16%.
Common wrong answers
- If you answered 2
- 2 is the coefficient of t, not a percentage.
- If you answered 4
- 4% is the growth per half-year, since the exponent 2t counts half-years.
- If you answered 8
- 8% is 2 × 4, ignoring compounding.
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