[zeion]

Hi,
How can I get a function from this table? I know it doesn't match any exact polynomials, but the textbook is asking for an "equation to model the data". How should I do that?

[macosxnerd101]

Perhaps this would be better modeled as a sinusoidal function, in the form f(t) = Asin(bt + c) + h.

This tutorial covers them more in-depth.

[zeion]

I don't think that's what they're asking for since the chapter was about polynomials and inequalities.. I know that isn't much help. Would it be acceptable to only use a few points? (ie. the first 3) and fit that into say a quadratic equation?

Here's are the questions:


This is for part b.

[peace_fixation]

You can use polynomial interpolation. The basic premise is, you have n data points. You can find a polynomial of degree n-1 that passes through all n data points. (There are many ways to interpolate, this is just one and it's pretty easy)

Your data points, as tabled, give you 7 (x,y) coordinates: (x1,y1),(x2,y2),(x3,y3),...,(x7,y7)

Formulate 7 polynomials of degree 6:

a(x1)^6 + b(x1)^5 + c(x1)^4 + d(x1)^3 + e(x1)^2 + f(x1) + g = y1
a(x2)^6 + b(x2)^5 + c(x2)^4 + d(x2)^3 + e(x2)^2 + f(x2) + g = y2
a(x3)^6 + b(x3)^5 + c(x3)^4 + d(x3)^3 + e(x3)^2 + f(x3) + g = y3
...
a(x7)^6 + b(x7)^5 + c(x7)^4 + d(x7)^3 + e(x7)^2 + f(x7) + g = y7

Substitute the values for x1,x2,...,x7 and y1,y2,...,y7 from your table into the above equations.

Now you have 7 equations in 7 unknowns (a,b,c,d,e,f,g), solve for the 7 unknowns. You can do this by putting them in matrix form and using Gaussian elimination, or any other method you know (Wolfram Alpha can do it for you).


Once you have the 7 unkowns, you can make a general polynomial:

a(x)^6 + b(x)^5 + c(x)^4 + d(x)^3 + e(x)^2 + f(x) + g = y

Substitute in your values for a,b,c,d,e,f,g.

Now you have a polynomial equation of degree 6 that is guaranteed to pass through all of your data points. Graph it onto an appropriate domain to get the information you need.

This post has been edited by peace_fixation: 19 October 2012 - 08:41 PM

[lordofduct]

Thing is, that's not what they're learning right now...

It appears, from the question, that you just need to match it up with the base functions that you've learned recently.

You've plotted the points right?

Look at the points and try and draw a curve that passes through them functionally (from left to right), what kind of curve does this look like? Match it to the generic functions you've learned in this chapter. What values would you have to modify the generic function by to get these values... translating it horizontally or vertically, scaling it, etc.

[peace_fixation]

Fair point, I kinda jumped the gun.

zeion, take lordofduct's advice, there is a simpler function you can choose to fit these data points, at least approximately although it should be very close.