The correct answer is C because when sales have a relatively constant growth rate over time, the log-linear model (lnSₜ = ln(β₀ + β₁ × t)) is most appropriate. This model transforms the data to linearize exponential growth patterns, where the coefficient β₁ represents the constant growth rate.

Key points:

• Option A (Sₜ = β₀ + β₁ × Sₜ₋₁): This is an autoregressive model that assumes current sales depend on previous period's sales, not suitable for constant growth rates.
• Option B (Sₜ = β₀ + β₁ × t): This is a simple linear trend model that assumes constant absolute increases, not constant percentage growth rates.
• Option C (lnSₜ = ln(β₀ + β₁ × t)): This log-linear model captures constant growth rates as the coefficient β₁ represents the growth rate when the dependent variable is logged.
• Option D (Sₜ = β₀ + β₁ × t + β₂ × t²): This quadratic trend model allows for accelerating or decelerating growth, not constant growth rates.

Mathematical reasoning: When growth rate is constant, sales follow: Sₜ = S₀ × (1 + g)ᵗ, where g is the constant growth rate. Taking natural logs: ln(Sₜ) = ln(S₀) + t × ln(1 + g), which is linear in t with slope ln(1 + g) ≈ g for small g.