Respuesta :

Answer:

[tex]y=12(3)^x[/tex]

Explanation:

Given the form of the exponential function:

[tex]y=ab^x[/tex]

In the pair: (0,12)

[tex]\begin{gathered} x=0,y=12 \\ \implies12=a\times b^0 \\ \implies12=a\times1 \\ a=12 \end{gathered}[/tex]

Substituting a=12, and the point (1,36):

[tex]\begin{gathered} y=ab^x \\ 36=12\times b^1 \\ 12b=36 \\ b=\frac{36}{12} \\ b=3 \end{gathered}[/tex]

Thus, the exponential function is:

[tex]y=12(3)^x[/tex]

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