We use the first point given (0, 14) to solve a in terms of b. We have
[tex]\begin{gathered} 14=ab^0 \\ 14=a \end{gathered}[/tex]We use the second point given (3,3024) to solve for the value of b,
[tex]3024=ab^3[/tex]Substitute the value of a solved by the equation above on the equation above and solve
[tex]\begin{gathered} 3024=14b^3 \\ b=\sqrt[3]{216} \\ b=6 \end{gathered}[/tex]Hence, the exponential function is written as
[tex]f(x)=14(6)^x[/tex]
