{Use of Tech} Fuel economy Sup​​pose 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.
a. Graph and interpret the mileage function.

Verified step by step guidance

1. Identify the function m(g) = 50g - 25.8g² + 12.5g³ - 1.6g⁴, which represents the mileage based on the gallons of gas g.
2. Determine the domain of the function, which is given as 0 ≤ g ≤ 4, meaning we will only consider values of g from 0 to 4.
3. Calculate the values of m(g) at key points within the domain, such as g = 0, 1, 2, 3, and 4, to understand how mileage changes with gas consumption.
4. Use the calculated values to plot the points on a graph, with g on the x-axis and m(g) on the y-axis, to visualize the relationship between gas and mileage.
5. Interpret the graph by analyzing the shape of the curve, identifying any maximum or minimum points, and discussing what these points mean in the context of fuel economy.