Answer:
[tex]f(x)=\dfrac{3}{2}(2)^x[/tex]
Step-by-step explanation:
The given sequence is
{3, 6, 12, 24, 48, 96, ...}
It means f(x)=3, 6, 12, 24, 48, 96, ... for x=1,2,3,4,5,6,.. respectively.
We need to find non-linear function in the form
[tex]f(x)=ab^x[/tex] ...(1)
We know that f(x)=3 for x=1.
[tex]3=ab^1[/tex] ....(i)
We know that f(x)=6 for x=2.
[tex]6=ab^2[/tex] ....(ii)
Divide equation (ii) by (i).
[tex]\dfrac{6}{3}=\dfrac{ab^2}{ab}[/tex]
[tex]2=b[/tex]
Substitute b=2 in equation (1).
[tex]3=a(2)^1[/tex]
[tex]\dfrac{3}{2}=a[/tex]
Substitute [tex]a=\dfrac{3}{2}[/tex] and [tex]b=2[/tex] in (1).
[tex]f(x)=\dfrac{3}{2}(2)^x[/tex]
Therefore, the required function is [tex]f(x)=\dfrac{3}{2}(2)^x[/tex].
