The equation representing the height of the plant on day n, given the constant growth rate, is h(n) = 1.75n + 0.25.
The question involves creating an equation to represent the growth of a plant over time based on provided data. The data shows the heights of a plant on different days, indicating that it grows at a constant rate each day. To establish an equation, we can calculate the rate of growth between any two days and use this rate to determine the slope of the linear equation. The provided data points are Day 1: 2 cm, Day 3: 6 cm, and Day 5: 9 cm. We could take the difference between Day 5 and Day 1, which is (9 cm - 2 cm) / (5 - 1) = 1.75 cm per day. Therefore, the slope (rate of growth) is 1.75 cm/day. The equation to represent the height h(n) of the plant on day n would be h(n) = 1.75n + b, where b is the y-intercept. Given that the height on Day 1 is 2 cm, we can substitute n = 1 to find b. The equation becomes h(1) = 1.75(1) + b, which simplifies to 2 = 1.75 + b. Solving for b gives us b = 2 - 1.75 = 0.25. Now we can write the final equation as h(n) = 1.75n + 0.25, which represents the height of the plant on day n.