Answer: lnSₜ = ln(β₀ + β₁ × t)

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.

Author: Nikitesh Somanthe