A population starts at 1000 and doubles every 3 years. Which expression models P(t) for t years?

• A. P(t) = 1000·2^{t}
• B. P(t) = 1000·(1/2)^{t/3}
• C. P(t) = 1000·2^{t/3}
• D. P(t) = 1000·2^{-t/3}

Answer: (C)

Exponential growth with a constant doubling time uses the idea that every fixed period multiplies the amount by 2. The number of doubling periods that occur in t years is t divided by the doubling time. Here the population starts at 1000 and doubles every 3 years, so the model is P(t) = 1000 · 2^{t/3}. This ensures the initial value matches (t = 0 gives 1000) and after each 3-year step the population doubles (t = 3 gives 2000, t = 6 gives 4000, etc.). Other forms either would imply doubling each year, halving every 3 years, or both, which contradicts the given doubling rate, so the correct expression is the one with 2^{t/3}.