the speed of a car traveling on a highway is being recorded once per second for two minutes. during this…

the speed of a car traveling on a highway is being recorded once per second for two minutes. during this time interval, the car gradually speeds up slightly to pass another vehicle, then the car returns to its original speed. the recorded speed of the car with respect to time can be modeled by linear, quadratic, and exponential functions. for each of the three models, their residuals are small and are without pattern. which of the following conclusions is best? a a linear model is best based on contextual clues. b a quadratic model is best based on contextual clues. c an exponential model is best based on contextual clues. d contextual clues fail to help in selecting a model for this contextual situation.

the speed of a car traveling on a highway is being recorded once per second for two minutes. during this time interval, the car gradually speeds up slightly to pass another vehicle, then the car returns to its original speed. the recorded speed of the car with respect to time can be modeled by linear, quadratic, and exponential functions. for each of the three models, their residuals are small and are without pattern. which of the following conclusions is best? a a linear model is best based on contextual clues. b a quadratic model is best based on contextual clues. c an exponential model is best based on contextual clues. d contextual clues fail to help in selecting a model for this contextual situation.

Answer

Brief Explanations:

Since the residuals for linear, quadratic, and exponential models are all small and without pattern, contextual clues (like the car speeding up and then returning to original speed) do not give an edge to any one of these models. A linear model would imply a constant rate of change (which isn't the case as the car first speeds up and then slows down). A quadratic model has a parabolic shape (which could potentially model the speeding - up and then slowing - down, but there's no clear indication that it's the best). An exponential model implies a multiplicative rate of change (which also isn't clearly indicated).

Answer:

D. Contextual clues fail to help in selecting a model for this contextual situation.