Finding the curve of best fit

Mar 2017
358
3
Massachusetts
Hi,

I hope someone can help me with the following question:

Screen Shot 2017-06-30 at 11.07.08 AM.png

And this is the data:

Screen Shot 2017-06-30 at 11.07.35 AM.png

I used the online graphing technology program called, MyCurveFit, and I got the following data for the following functions:
Quadratic: y = 395.3571 - 11.28571*x + 0.1285714*x^2
Exponential(basic): y = 57.99277 + 339.1588*e^(-0.03634446*x)
Linear: y = 3263.235*x - 6380067

These equations that I listed above are pretty far off from what it seems to the textbook's, as follows:
Screen Shot 2017-06-30 at 11.13.14 AM.png

Can anyone tell why my equations are so far off from the textbook's?
 

HallsofIvy

MHF Helper
Apr 2005
20,249
7,909
What data did you put into this program? When x= 0, the quadratic "approximation" you list gives y= 395.397, the exponential gives y= 397.1515, and the linear gives y= - 6380067. None of those are really close to 400 and the last is simply ludicrous. Have you tried doing the problem yourself rather than just handing it over to a program?
 
Mar 2017
358
3
Massachusetts
Yeah, I just tried solving it for myself and I got the correct formulas for exponential and linear. I get a different formula for quadratic, however. I know that the quadratic equation form is y=ax^x + bx + c. I ended up getting the quadratic formula of y = -1.56x^2 - 5.2 + 400... which is pretty different from the textbook's solution even after I placed mine into vertex form.

The reason why I'm trying to learn how to use a graphing program is because when data sets become more complex, it will be a lot easier to use a program. I hope that you can help teach me.