Answer:
[tex]f(x) =3 * (4)^x[/tex]
Step-by-step explanation:
Given
[tex](x_1, y_1) = (1,12)[/tex]
[tex](x_2, y_2) = (0,3)[/tex]
Required
The function of the graph (exponential function)
An exponential function is represented as:
[tex]f(x) = ab^x[/tex]
For [tex](x_1, y_1) = (1,12)[/tex], we have:
[tex]12 = a * b^1[/tex]
[tex]12 = a * b[/tex]
[tex]12 = a b[/tex]
For [tex](x_2, y_2) = (0,3)[/tex]
[tex]3 = a * b^0[/tex]
[tex]3 = a * 1[/tex]
[tex]3 = a[/tex]
[tex]a = 3[/tex]
Substitute: [tex]a = 3[/tex] in [tex]12 = a b[/tex]
[tex]12 = 3 * b[/tex]
Divide both sides by 3
[tex]4 = b[/tex]
[tex]b =4[/tex]
So, we have:
[tex]f(x) = ab^x[/tex]
[tex]f(x) =3 * (4)^x[/tex]
