Final answer:
The relationship between the height and volume of water in a bottle depends on the bottle's shape; for a cylindrical bottle, it would typically be a direct variation where height increases proportionally with volume.
Step-by-step explanation:
The question asks how the height of water in a bottle varies with the volume of water in the bottle over the interval from v = 0 to v = 1.5. To determine the relationship, you would need additional information about the shape of the bottle. However, the options given (direct, inverse, constant, and exponential variation) can be understood in a general sense:
- Direct Variation: This would imply that as the volume of water increases, the height of water in the bottle also increases proportionally.
- Inverse Variation: This would imply that as the volume of water increases, the height of water in the bottle decreases, and vice versa.
- Constant Variation: This would imply that the height of water remains the same, regardless of the volume change, which is not typical unless the bottle has an unusual shape.
- Exponential Variation: This would imply that the height of water changes at an exponential rate as the volume of water changes.
Without specific information on the shape of the bottle, it's not possible to definitively choose one of these options. Typically, for a cylindrical bottle, the relationship would be a direct variation as the height of the water would directly correlate with the volume of water until the bottle is full.