The world’s population will double in the next 20 years.

Question

BlackTom AI · Accepted Answer

Doubling in 20 years requires an annual growth rate of about 3.5%, which is far above present and projected rates.

Relevant concepts:
- Doubling time and exponential growth: population grows roughly as P(t) = P0(1 + r)^t (discrete) or P(t) = P0 e^{rt} (continuous).
- Current global growth rates and UN population projections reflect fertility decline and demographic transition.

Step-by-step calculation:
1. Using discrete annual growth: (1 + r)^20 = 2.
2. Solve for r: r = 2^{1/20} − 1.
3. Compute 2^{1/20} = e^{ln(2)/20}. ln(2) ≈ 0.693147, so ln(2)/20 ≈ 0.034657.
4. e^{0.034657} ≈ 1.03527, so r ≈ 0.03527 = 3.527% per year.
(Using continuous growth, r = ln(2)/20 ≈ 0.034657 = 3.466% per year; both show about 3.5% annual growth required.)

Compare with reality:
- The current global population is ~8 billion. Doubling in 20 years would give ~16 billion by ~2044.
- Recent global annual growth rates are about 1% or less (roughly 0.8–1.1% in recent years) and declining due to lower fertility and aging populations.
- At 1% annual growth, doubling time ≈ ln(2)/0.01 ≈ 69.3 years (rule of 70: 70/1 ≈ 70 years), not 20 years.
- UN World Population Prospects (medium variant) projects ~9.7 billion by 2050 — far short of 16 billion.

Why "True" is incorrect:
- It implies an implausibly large and sudden increase in global fertility or decline in mortality that contradicts observed trends and expert projections.
- No demographic evidence supports a jump to ~3.5% sustained global growth for 20 years.

Conclusion: The statement is False, which matches the provided answer.

The world’s population will double in the next 20 years.判断题

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