Answer: [tex]f(x)=4^x[/tex]
Step-by-step explanation:
The general exponential function is given by :-
[tex]f(x)=Ab^x[/tex], where A is initial amount , b is multiplicative growth rate and x is time period.
Also, the multiplicative growth rate is the common ratio of the consecutive terms.
From the given table , [tex]b=\dfrac{256}{64}=4[/tex]
Substitute, x = 3 , f(x)=64 and b=4 , we get
[tex]64=A(4)^3\\\\\Rightarrow\ 64=A(64)\\\\\Rightarrow\ A=1[/tex]
Hence, the exponential function represents the data in the table is
[tex]f(x)=(1)(4)^x\\\\\Rightarrow\ f(x)=4^x[/tex]