Answer :
The equation of an exponential function is of the form
[tex]f(x)=a(b)^x[/tex]we know that
For x=0 -----> f(x)=7
substitute
[tex]\begin{gathered} 7=a(b)^0 \\ 7=a(1) \\ a=7 \end{gathered}[/tex]substitute the value of a
[tex]f(x)=7(b)^x[/tex]Remember that
For x=3 ----> f(x)=56
substitute
[tex]\begin{gathered} 56=7(b)^3 \\ b^3=\frac{56}{7} \\ \\ b^3=8 \\ b^3=2^3 \\ b=2 \end{gathered}[/tex]The equation is given by
[tex]f(x)=7(2)^x[/tex]