Respuesta :
The general form of an exponential function is,
[tex]f(x)=ab^x[/tex]Given that f(3)=11 and f(11)=63 implies,
[tex]\begin{gathered} 11=ab^3\ldots\ldots(1) \\ 63=ab^{11}\ldots\ldots(2) \end{gathered}[/tex]Divide equation (2) by (1) implies,
[tex]\begin{gathered} \frac{63}{11}=b^8 \\ b=1.24 \end{gathered}[/tex]Then, the value of a is,
[tex]\begin{gathered} 11=a\times1.24^3 \\ a=5.76 \end{gathered}[/tex]Therefore, the function is,
[tex]f(x)=5.76\times1.24^x[/tex]Find the value of f(6).
[tex]\begin{gathered} f(6)=5.76\times1.24^6 \\ =20.93 \end{gathered}[/tex]Therefore, the answer is 20.93
