4. Work Prediction14.8=a(1950-1970)^2+13.4 The Data that I received from the graph was14.8=a(20)^2+13.4 inaccurate, since it gave me an incorrect14.8=400a+13.4 equation. When I tried to use the equation excel-13.4 -13.4 gave me, I received the answer of -17 for my1.4=400a MPG for a 2011. Which is obviously incorrect, so I0.0035=a had to create my own equation. This is becausey= 0.0035(x-1970)^2+13.4 excel is program created by humans and peopley= 0.035(2011-1970)^2 make mistakes. So to predict how much a 2011y= 0.0035(41)^2+13.4 car would get for gas mileage according to they= 0.0035(41)^2+13.4 data, I had to create my own equation. I did thisy= 0.0035(1681)+13.4 by using the standard quadratic equation of y=a(x-y= 19.2835 – round to 19.3 h)^2. I then used the vertex (1970, 13.4) as my h19.3 mpg predicted for a and k, and the point (1950, 14.8) as my x and y.2011 car 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.
5. 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.
6. Gas Mileage Graph
7. How Speed affects Gas MileageUsing the graph for how speed affects gas mileage, I was able to figureout that at 35 MPH the car would get 29 MPG. I figured this out byusing the graphs equation of y= -0.0108x^2+0.9811x+8.0481. I thenplugged in the 35 MPH for x and I came up with 29 for my MPG. So thisshows that when you drive at 35 MPH, you get a gas mileage of 29MPH. Also the speed for which the car’s gas mileage is the maximumis 45 MPH. I figured this out by using the equation of –b/2a. I pluggedin the -b, -0.9811 from the data’s equation into maximum equationand divided it by the a, -0.0108 multiplied by 2. This then gave me thespeed of 45 MPH. I also could have figured this out though, by lookingat my data and seeing that after 45 MPH, at 65 MPH the MPGdecreased for the first time in my data. Showing that the faster youdrive the worst gas mileage you get.
8. SpeechOverall, from the data I gathered and graphs I created, I saw that as we havecome more into the future, the gas mileage for car has improved. These daysin 2011, there are even hybrid, fuel efficient cars that are designed specificallyto get better gas mileage. In the case of the car, I chose to compare to mypredicted MPG for a 2011 car to, the Honda CR-Z is actually a fuel efficienthybrid that gets really good gas mileage. This car gets 34 MPG, and myprediction was only 19.3 MPG, an almost 15 miles difference. If I had chosen anon hybrid car like a 2011 Toyota Camry for example, it would have gotten 26MPG. Which is still, almost 7 miles more, which is a significant increaseconsidering that according to my data, over 10 years the gas mileage only wentup about 1 or 2 miles per gallon. Also from my data, I was able to prove that thefaster you drive the worse gas mileage you get. Also overall, while finding mydata for the gas mileage per year, I encountered problems with the excelprogram it’s self, and I was able to learn the importance of checking for humanerror, even while working on the computer.