Luke has two children. Each of Luke's children has two children. Each child after that has two children. If Luke's children represent the first generation of the family, which type of function would best model the number of children in the nth
generation of the family?

A. Linear function of n
B. Quadratic function of n
C. Square root function of n
D. Exponential function of n

Table #1:

Using the first two points (2,1) and (5,3)

You get (x-2)/3 = (y-1)/2

But then the 3rd point (8,7) does not work, so this is not linear.

Table #2

Using the first two points (1,10) and (2,13)

You get x-1 = (y-10) /3

But then the 3rd point (3,18) does not work so this is also not linear.

Table #3

Using the first two points (2,1) and (4,6)

You get x-2 /2 = y-1 /5

And all the other points will work with this, which makes this table linear.

Rewrite the equation to get y = 5/2x-4