We are asked to write a power function whose graph includes the points (3,14) and (9,44):

`14=a3^b,44=a9^b`

From the first equation we get:

`a=14/(3^b)`

Then

`44=(14/(3^b))*9^b`

`44=14*3^b`

`3^b=22/7`

`b=(ln(22/7))/(ln(3))~~1.042`

We can now solve for a to get:

`a=14/(3^b)=14/(3^(ln(22/7)/ln(3)))=49/11~~4.455`

The model is `y=49/11x^1.042`