Miles Per Gallon

By: Jessica Freeman

Class: F

Data

Year MPG

1950 14.8

1960 13.9

1970 13.4

1980 13.5

1990 15.5

1995 18.3

Graph

PredictionThe Data that I received from the graph was inaccurate, since it gave me an incorrect equation. When I tried to use the equation excel gave me, I received the answer of -17 for my MPG for a 2011. Which is obviously incorrect, so I had to create my own equation. This is because excel is program created by humans and people make mistakes. So to predict how much a 2011 car would get for gas mileage according to the data, I had to create my own equation. I did this by using the standard quadratic equation of y=a(x-h)^2. I then used the vertex (1970, 13.4) as my h and k, and the point (1950, 14.8) as my x and y. After plugging this into the equation of y=a(x-h)^2, I received 0.0035 as my a. I then used my a to come up with the correct equation of, y= 0.0035(x-1971)^2+13.4. I then in plugged 2011 as my x and I got 19.3 as my predicted MPG for a 2011 car.

Work14.8=a(1950-1970)^2+13.414.8=a(20)^2+13.414.8=400a+13.4-13.4 -13.41.4=400a0.0035=a y= 0.0035(x-1970)^2+13.4y= 0.035(2011-1970)^2y= 0.0035(41)^2+13.4 y= 0.0035(41)^2+13.4 y= 0.0035(1681)+13.4 y= 19.2835 – round to 19.319.3 mpg predicted for a 2011 car

Actual MPG for 2011 Car

A 2011 Honda CR-Z actually gets 34 MPG. This because the car is actually a hybrid and is made to be more fuel efficient.

Gas Mileage Graph

How Speed affects Gas Mileage

Using the graph for how speed affects gas mileage, I was able to figure out that at 35 MPH the car would get 29 MPG. I figured this out by using the graph's equation of y= -0.0108x^2+0.9811x+8.0481. I then plugged in the 35 MPH for x and I came up with 29 for my MPG. So this shows that when you drive at 35 MPH, you get a gas mileage of 29 MPH. Also the speed for which the car’s gas mileage is the maximum is 45 MPH. I figured this out by using the equation of –b/2a. I plugged in the -b, -0.9811 from the data’s equation into maximum equation and divided it by the a, -0.0108 multiplied by 2. This then gave me the speed of 45 MPH. I also could have figured this out though, by looking at my data and seeing that after 45 MPH, at 65 MPH the MPG decreased for the first time in my data. Showing that the faster you drive the worst gas mileage you get.

SpeechOverall, from the data I gathered and graphs I created, I saw that as we have come more into the future, the gas mileage for car has improved. These days in 2011, there are even hybrid, fuel efficient cars that are designed specifically to get better gas mileage. In the case of the car, I chose to compare to my predicted MPG for a 2011 car to, the Honda CR-Z is actually a fuel efficient hybrid that gets really good gas mileage. This car gets 34 MPG, and my prediction was only 19.3 MPG, an almost 15 miles difference. If I had chosen a non hybrid car like a 2011 Toyota Camry for example, it would have gotten 26 MPG. Which is still, almost 7 miles more, which is a significant increase considering that according to my data, over 10 years the gas mileage only went up about 1 or 2 miles per gallon. Also from my data, I was able to prove that the faster you drive the worse gas mileage you get. Also overall, while finding my data for the gas mileage per year, I encountered problems with the excel program it’s self, and I was able to learn the importance of checking for human error, even while working on the computer.