Final answer:
The correct function for the weight M of the oil bottle after Sophia uses V milliliters is M = -0.95V + 590, which represents a linear relationship between the volume of oil used and the weight of the bottle. However, this correct function is not included among the provided answer choices, indicating a potential issue with the question.
Step-by-step explanation:
The question involves creating a function M(V) that describes the weight of a bottle of oil as a function of the volume of oil used by Sophia. Initially, the bottle with oil weighs 590 grams. After Sophia uses 200 milliliters of oil, the remaining bottle of oil weighs 400 grams. To obtain the function, we should consider two points: (0, 590) and (200, 400), where the first value is the volume of oil used in milliliters, and the second value is the weight of the bottle and remaining oil in grams.
The weight M decreases linearly with the volume V used. The change in weight 590g - 400g = 190g corresponds to the change in volume of 200mL. Therefore, the slope of the line (change in weight per unit volume) is -190g/200mL, which simplifies to -0.95 g/mL. The bottle itself has a constant weight, which is the weight left when all oil is used, that is 400g minus the weight of 200mL of oil (200mL × 0.95g/mL). This yields 190g, which is the intercept of the function. Thus, the correct function is M = -0.95V + 590, which is not listed among the options. Hence, either there is a mistake in the provided options, or further information is required to correctly match the given answer choices.