nonlinear equation for a set of points???

[helpwithmath22]

I need help finding the nonlinear equation that describes the set of six points I have.

the points I have are (6.14, 97.57), (7.03, 90.54), (8.55, 81.99), (10.52, 71.47), (14.97, 56.50), (24.62, 31.88)

The dependant variable will be the y value and the indepandant value will be the x.

In other words we are deriving the y from x placed into an equation.

 

[stapel]

I need help finding the nonlinear equation that describes the set of six points I have.

Are you told what sort of equation they're looking for, or will any polynomial do?

 

[Deleted member 4993]

I need help finding the nonlinear equation that describes the set of six points I have.

the points I have are (6.14, 97.57), (7.03, 90.54), (8.55, 81.99), (10.52, 71.47), (14.97, 56.50), (24.62, 31.88)

The dependant variable will be the y value and the indepandant value will be the x.

In other words we are deriving the y from x placed into an equation.

There are several ways to accomplish this. What method/s have you been taught?

 

[HallsofIvy]

You have six given values so could use them to construct 6 equations to be solved for 6 unknowns.

For example you could set \(\displaystyle y= ax^5+ bx^4+ cx^3+ dx^2+ ex+ f\)
Then, knowing that y(6.14)= 97.57, you would have \(\displaystyle 97.57= a(6.14^5)+ b(6.140^4)+ c(6.14^3)+ d(6.14^2)+ e(6.14)+ f\) or 8726.5354185824a+ 1421.25984016b+ 231.475544c+ 37.6996d+ 6.14e+ f= 97.57.

Doing that with the other 5 points will give you 6 linear equations to solve for a, b, c, d, e, and f.

Or you could write \(\displaystyle y= ae^{bx}+ ce^{dx}+ ee^{fx}\). Again, replacing x and y with the 6 points given will 6 equations to solve.

Yet, another: \(\displaystyle y= acos(bx)+ c cos(dx)+ e cos(fx).\)