It's geometric sequence:
[tex]a_1=1.2,\ a_2=3,\ a_3=7.5,\ a_4=18.75,\ ....[/tex]
Calculate the common ratio:
[tex]r=\dfrac{a_{n+1}}{a_n}\to r=\dfrac{3}{1.2}=2.5[/tex]
The explicit formula of geometric sequence:
[tex]a_n=a_1r^{n-1}\to f(x)=a_1r^{x-1}[/tex]
Substitute:
[tex]a_1=1.2,\ r=2.5\\\\f(x)=1.2\left(2.5)^{x-1}[/tex]
Answer: "f(x) = 1.2(2.5)x-1"
