1. **Determine the height of the plant after 4 weeks using** $H(t) = 2t^3 - 5t^2 + 3t + 1$. Substitute $t=4$: $$H(4) = 2(4)^3 - 5(4)^2 + 3(4) + 1 = 2(64) - 5(16) + 12 + 1 = 128 - 80 + 12 + 1 = 61$$ So, the height after 4 weeks is 61 cm. 2. **Find the average rate of change of the plant's height between weeks 1 and 3.** The average rate of change is given by: $$\frac{H(3) - H(1)}{3 - 1}$$ Calculate $H(3)$: $$H(3) = 2(3)^3 - 5(3)^2 + 3(3) + 1 = 2(27) - 5(9) + 9 + 1 = 54 - 45 + 9 + 1 = 19$$ Calculate $H(1)$: $$H(1) = 2(1)^3 - 5(1)^2 + 3(1) + 1 = 2 - 5 + 3 + 1 = 1$$ Now compute the average rate: $$\frac{19 - 1}{2} = \frac{18}{2} = 9$$ The average rate of change is 9 cm/week. 3. **Explain the impact of the coefficient of the $t^3$ term in $H(t) = 2t^3 - 5t^2 + 3t + 1$.** The coefficient 2 in front of $t^3$ affects the overall growth rate and the shape of the cubic function, influencing how quickly the plant's height changes as time progresses. It does not determine the number of critical points or vertical shift directly. Therefore, it influences the overall growth rate of the plant. 4. **What is a central angle in a circle?** A central angle is an angle whose vertex is at the center of the circle and whose sides are radii. 5. **Find the measure of the inscribed angle $\angle APB$ that subtends arc AB measuring 120°.** The inscribed angle is half the measure of the arc it subtends: $$\angle APB = \frac{120^\circ}{2} = 60^\circ$$ **Final answers:** 11. Height after 4 weeks: 61 cm (d) 12. Average rate of change: 9 cm/week (d) 13. Coefficient of $t^3$ influences overall growth rate (c) 14. Central angle vertex at center of circle (d) 15. Inscribed angle measure: 60° (d)