Answer:
g(x) = [tex]12.(\frac{3}{4})^x[/tex]
Step-by-step explanation:
Exponential function g has been represented by the table attached,
Equation of the exponential function is,
g(x) = [tex]a.(b)^x[/tex]
Now we substitute the values of x and g(x) from the table,
For a point (0, 12),
12 = [tex]a(b)^0[/tex]
a = 12
For another point (1, 9),
9 = [tex]a.(b)^1[/tex]
9 = a × b
9 = 12 × b
b = [tex]\frac{9}{12}[/tex]
b = [tex]\frac{3}{4}[/tex]
Therefore, equation of the exponential function will be,
g(x) = [tex]12.(\frac{3}{4})^x[/tex]
