Respuesta :
The general form of the exponential function is:
[tex]f(x)=a\cdot b^x[/tex]we will find the equation of the exponential function which passes through the points (0, 36) and (2, 1)
So,
when x = 0, f(0) = 36
[tex]\begin{gathered} 36=a\cdot b^0 \\ 36=a\cdot1 \\ a=36 \end{gathered}[/tex]and when x = 2, f(x) = 1
Using the substitution with a = 36
So,
[tex]\begin{gathered} 1=36\cdot b^2 \\ b^2=\frac{1}{36} \\ \\ b=\sqrt[]{\frac{1}{36}}=\frac{1}{6} \end{gathered}[/tex]So, the answer will be the equation of the function is:
[tex]f(x)=36\cdot(\frac{1}{6})^x[/tex]