The general form of an exponential function is the following
[tex]\begin{gathered} y=ab^x \\ a\ne0 \\ b>1 \end{gathered}[/tex]
we can find the values for a and b using the known values for x and y. First, notice that when x = 0, y =51, then, if we put these values on the general form, we get:
[tex]\begin{gathered} 51=ab⁰=a(1)=a \\ \Rightarrow a=51 \end{gathered}[/tex]
next, we have that when x = -1, y = 17. We also know now that a = 51, then, using this information, we can find the value of b:
[tex]\begin{gathered} 17=51b^{-1} \\ \Rightarrow17=\frac{51}{b} \\ \Rightarrow17b=51 \\ \Rightarrow b=\frac{51}{17}=3 \\ b=3 \end{gathered}[/tex]
therefore, the exponential function is y = 51(3)^x
