{Use of Tech} Fuel economy Suppose you own a fuel-efficient ...

Question

{Use of Tech} Fuel economy Suppose you own a fuel-efficient hybrid automobile with a monitor on the dashboard that displays the mileage and gas consumption. The number of miles you can drive with g gallons of gas remaining in the tank on a particular stretch of highway is given by m(g) = 50g−25.8g²+12.5g³−1.6g⁴, for 0≤g≤4.
b. Graph and interpret the gas mileage m(g)/g.

b. Graph and interpret the gas mileage m(g)/g.

Accepted Answer

Mark owns an electric vehicle with a dashboard monitor that displays the driving range based on battery charge. The number of miles you can drive with kilowatt hours of battery charge remaining is given as RC equals 60C minus 30.5 C2 plus 14.2 CQed minus 2.1Cs to the 4th. For C between 0 and 5, graph and interpret the energy efficiency function, ROC divided by C using a graphing calculator. Now, for this function, we have RFC divided by C. And we can just plug in our equation just as we see it. We have 60C. Minus 30.5 C squared. Plus 14.2 C cubed minus 21, or rather 2.1 C to the fourth. All divided by C. No, we can cancel out a C for every one of our terms. We have 60C, which loses a C. Our C2 loses the C, C cube loses a C, becomes C2, and C of the 4th becomes C to the third. Our resulting function is 60. Minus 30.5 C plus 14.2 C squared, minus 2.1 C3. Now, this is our function, and on the left here is its respective graph. So, Let's interpret what the graph is telling us. Our kilowatt hours are first between 0 and 5. You notice We have a minimum point. Right in the middle of 1 and 2. At about 1.8, and a maximum point. Right between 2 and 3. At about 2.7. We can see then, our efficiency. First of all, is higher. At lower charge levels. We can see this because our efficiency is 60. When the charge is 0. And as the charge increases, our graph slowly decreases. We can also then tell That the efficiency. Decreases on the interval. 0 To 1.8 And 2.7. To 3.5 based on the graph. We can see this because our energy efficiency, the output, is going down. Until we get to 1.8. Efficiency increases. From 1.8 to 2.7. We can see that the graph very slightly goes up between those two values. OK, I hope that helps you solve the problem. Thank you for watching. Goodbye.

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