Final answer:
The correct equation to calculate the height of the water in the pond after x hours of rain, given the data that the water height increases by 0.5 feet each hour, is h(x) = 0.5x + 3.
Step-by-step explanation:
To write an equation that calculates the height of the water in the pond after x hours of rain, we need to find a linear relationship between time and water height based on the provided data: after 2 hours, the water is 4 feet deep, and after 3 hours, it is 4.5 feet deep. The change in water height is 0.5 feet over the course of 1 hour (from 4 feet to 4.5 feet), which indicates a rate of change of 0.5 feet per hour. To find the starting height, we can extrapolate back one hour from the 2-hour mark. This suggests that after 1 hour, the height would have been 4 feet - 0.5 feet = 3.5 feet, and after 0 hours (the start), the height would be 3 feet (subtract another 0.5 feet).
Thus, the equation would be in the form of h(x) = 0.5x + 3, where h(x) represents the height of the pond after x hours. So the correct answer is (a) h(x) = 0.5x + 3.