Respuesta :
In this case, we need to find the constants a and b. We can find them by means of the given points.
By substituting point (0,8) into the exponential function, we have
[tex]8=a\cdot b^0[/tex]where y was equal to 8 and x was equalt to 0. Then, it yields,
[tex]\begin{gathered} 8=a\cdot1 \\ 8=a \end{gathered}[/tex]so, we found that a is 8.
Now, we can find b by substituting the other point with our last result. That is,
[tex]200=8\cdot b^2[/tex]where y was 200 and x was 2. So, by moving 8 to the left hand side,we get
[tex]\begin{gathered} \frac{200}{8}=b^2 \\ 25=b^2 \end{gathered}[/tex]then, b is given by
[tex]\begin{gathered} b=\sqrt[]{25} \\ b=5 \end{gathered}[/tex]Therefore, the exponential function is
[tex]y=8\times5^x[/tex]