Answer:
The exponential function is;
[tex]y=9(\frac{4}{3})^x[/tex]
Explanation:
Given that the function is an exponetial function.
It is of the form;
[tex]y=ab^x[/tex]
And the function contains the points;
[tex]\begin{gathered} (1,12) \\ \text{and} \\ (0,9) \end{gathered}[/tex]
so, substituting the values of x and y for each point;
[tex]\begin{gathered} 12=ab^1 \\ 12=ab\text{ -------1} \\ 9=ab^0 \\ 9=a\text{ ----------2} \end{gathered}[/tex]
dividing equation 1 by 2;
[tex]\begin{gathered} \frac{12}{9}=\frac{ab}{a} \\ b=\frac{12}{9} \\ b=\frac{4}{3} \\ \text{and } \\ a=9 \end{gathered}[/tex]
Therefore, substituting a and b, the equation gives;
[tex]\begin{gathered} y=ab^x \\ y=9(\frac{4}{3})^x \end{gathered}[/tex]
Therefore, the exponential function is;
[tex]y=9(\frac{4}{3})^x[/tex]
