1. **State the problem:** We are given a table of visitors to a website over days and asked: a. Whether the data represents exponential growth, decay, or neither. b. To predict the number of visitors after 47 days. 2. **Check for exponential growth or decay:** Exponential growth or decay means the ratio of visitors from one day to the next is constant. Calculate the ratios: $$\frac{12100}{11000} = 1.1, \quad \frac{13310}{12100} \approx 1.1, \quad \frac{14641}{13310} \approx 1.1$$ Since the ratio is consistently about 1.1 (greater than 1), this is exponential growth. 3. **Write the exponential growth formula:** $$V(t) = V_0 \times r^{t - t_0}$$ where $V_0$ is the initial visitors at day $t_0$, and $r$ is the growth rate. 4. **Identify values:** From the table, let $t_0 = 42$, $V_0 = 11000$, and $r = 1.1$. 5. **Calculate visitors at day 47:** $$V(47) = 11000 \times 1.1^{47 - 42} = 11000 \times 1.1^5$$ Calculate $1.1^5$: $$1.1^5 = 1.1 \times 1.1 \times 1.1 \times 1.1 \times 1.1 = 1.61051$$ So, $$V(47) = 11000 \times 1.61051 = 17715.61$$ Rounding to the nearest whole number: $$V(47) \approx 17716$$ --- 6. **Next problem:** Write an equation of the line passing through $(-5,6)$ and parallel to $y = -3x + 8$. 7. **Recall the slope of the given line:** The slope $m = -3$. 8. **Parallel lines have the same slope:** So the new line has slope $m = -3$. 9. **Use point-slope form:** $$y - y_1 = m(x - x_1)$$ where $(x_1, y_1) = (-5, 6)$. 10. **Substitute values:** $$y - 6 = -3(x + 5)$$ 11. **Simplify:** $$y - 6 = -3x - 15$$ $$y = -3x - 15 + 6$$ $$y = -3x - 9$$ **Final answers:** - a. The table shows exponential growth. - b. Visitors after 47 days: approximately 17716. - Equation of the line parallel to $y = -3x + 8$ passing through $(-5,6)$ is $y = -3x - 9$.