1. **Stating the problem:** We are given data of daily visitors $V(m)$ in millions over months $m$ since January 2009, and we want to model this data using an exponential decay function of the form $$y = ab^t$$ where $y$ is the number of daily visitors and $t$ is time in months. 2. **Formula and explanation:** The general exponential decay formula is $$y = ab^t$$ where: - $a$ is the initial amount (value at $t=0$), - $b$ is the decay factor per unit time (month), with $0 < b < 1$ for decay, - $t$ is the time in months. 3. **Identify initial value $a$:** From the table, at $m=0$, $V(0) = 25$ million, so $$a = 25$$ 4. **Find decay factor $b$ using another data point:** Using $m=6$, $V(6) = 20.5$ million, $$20.5 = 25 b^6$$ Divide both sides by 25: $$\frac{20.5}{25} = b^6$$ $$0.82 = b^6$$ 5. **Solve for $b$:** Take the sixth root (or raise both sides to the power $\frac{1}{6}$): $$b = 0.82^{\frac{1}{6}}$$ Calculate: $$b \approx e^{\frac{1}{6} \ln(0.82)} \approx e^{-0.0325} \approx 0.968$$ 6. **Write the model:** $$V(m) = 25 (0.968)^m$$ 7. **Interpretation:** This means the daily visitors decrease by about 3.2% each month. **Final answer:** $$\boxed{V(m) = 25 (0.968)^m}$$