The fuel efficiency, in miles per gallon, for a certain midsize car at various speeds, in miles per hour, is given in the table below. $$\begin{array} { | c | c | c | c | }
\hline \mathrm { mph } & \mathrm { mpg } & \mathrm { mph } & \mathrm { mpg } \
\hline 25 & 20 & 55 & 31 \
\hline 30 & 24 & 60 & 33 \
\hline 35 & 32 & 65 & 30 \
\hline 40 & 35 & 70 & 24 \
\hline 45 & 36 & 75 & 22 \
\hline 50 & 40 & & \
\hline
\end{array}$$ Find a quadratic model for these data and use it to predict the fuel efficiency of this car when it is traveling at a speed of 40 mph. Do not round any values in your calculations but round the final answer to the nearest tenth.
A)33.7 mpg
B)35.7 mpg
C)32.7 mpg
D)33.9 mpg
E)34.9 mpg

Question

The fuel efficiency, in miles per gallon, for a certain midsize car at various speeds, in miles per hour, is given in the table below. $$\begin{array} { | c | c | c | c | } 
\hline \mathrm { mph } & \mathrm { mpg } & \mathrm { mph } & \mathrm { mpg } \
\hline 25 & 20 & 55 & 31 \
\hline 30 & 24 & 60 & 33 \
\hline 35 & 32 & 65 & 30 \
\hline 40 & 35 & 70 & 24 \
\hline 45 & 36 & 75 & 22 \
\hline 50 & 40 & & \
\hline
\end{array}$$ Find a quadratic model for these data and use it to predict the fuel efficiency of this car when it is traveling at a speed of 40 mph. Do not round any values in your calculations but round the final answer to the nearest tenth.
A)33.7 mpg
B)35.7 mpg
C)32.7 mpg
D)33.9 mpg
E)34.9 mpg

Quizplus · Accepted Answer

The quadratic model that fits the given data points can be found using regression techniques, which typically involve statistical software or a calculator capable of performing regression analysis. For the purpose of this question, we assume such a model has been found and we are using it to predict the fuel efficiency at 40 mph. Given the data, the actual fuel efficiency at 40 mph is 35 mpg, which is a real data point from the table. However, since we're asked to predict using a quadratic model, slight variations from the actual data are expected due to the nature of modeling. The correct prediction, after applying the quadratic model and rounding to the nearest tenth, is 33.7 mpg, indicating that while the model provides a close approximation, it does not perfectly match the observed data at every point. This discrepancy highlights the limitations of using models for prediction, as they often generalize trends rather than perfectly fitting every data point.

The Fuel Efficiency, in Miles Per Gallon, for a Certain