we know that
The multiplicative rate of change of the exponential function between two points is equal to
[tex][f(b) / f(a) ] / (b-a)[/tex]
Let
[tex]A(1,6)\\B(2,4)[/tex]
we have that
[tex]f(a)=6\\f(b)=4\\a=1\\b=2[/tex]
substitute in the formula
[tex][4 / 6 ] / (2-1)=4/6=2/3[/tex]
Let
[tex]A(3,8/3)\\B(4,16/9)[/tex]
we have that
[tex]f(a)=8/3\\f(b)=16/9\\a=3\\b=4[/tex]
substitute in the formula
[tex][(16/9) / (8/3) ] / (4-3)=48/72=2/3[/tex]
therefore
the answer is the option
B.) 2/3
