Since clearly we can see that is not linear relation( straight line), let us find ratios of consecutive terms.
[tex]\frac{f(1)}{f(0)} = \frac{5.76}{4.8} = 1.2[/tex]
[tex]\frac{f(2)}{f(1)} = \frac{6.91}{5.76} =1.2[/tex]
[tex]\frac{f(3)}{f(2)} =\frac{8.29}{6.91} = 1.2[/tex]
This follows f(1)= 1.2*f(0)
f(2) = 1.2*f(1) = 1.2*1.2*f(0) = [tex]1.2^{2} * f(0)[/tex]
f(3) = 1.2*f(2) = [tex]1.2*1.2^{2} *f(0) = 1.2^{3} * f(0)[/tex]
Hence formula is f(x) = [tex]1.2^{x} * f(0)[/tex]
f(x) = [tex]4.8*(1.2)^{x}[/tex]
