the data (1,5), (3,16), (5,35), (7,67), (9,110) could be modeled as a linear relationship if

a) x is transformed to x^2
b) y is transformed to y^2
c) x is transformed to x^3
d) y is transformed to y^3

Question

the data (1,5), (3,16), (5,35), (7,67), (9,110) could be modeled as a linear relationship if

a) x is transformed to x^2
b) y is transformed to y^2
c) x is transformed to x^3
d) y is transformed to y^3

anonymous · Answer

is there more to the question ?

anonymous · Answer

nope that the whole question

mathmale · Answer

The wording of this problem is problematic (which of course is not the fault of the student).  When I saw the word "linear," I attempted to find the coefficients a and b for the linear function y = ax + b that would fit the data.  (In other words, if I were to take the first data point, (1,5), and substitute x=1 and y=5 into y =ax+b, the equation would have to be true, as it would for each and every one of the other data points.)

That failed.

So, I decided to use a quadratic (instead of linear) model:  y = ax^2 + bx + c.
Substituting the first point, (1,5), results in 5 = a*1^2 + b*1 + c.
Substituting two more points, one at a time, results in two additional LINEAR equations.

These three linear equations can be solved simultaneously to obtain values for a, b and c.

I ended up with a = 1, b = 3/2, and c = 5/2.

Try substituting these three coefficients into the general form y=a*x^2 + bx + c and verifying for yourself that substitution of any or all of the given points results in an equation that is true.

Want to discuss this question further?  If so, please ask.