Question

Write the function for the graph.

Answer 1

Answer:

$f(x) =3 * (4)^x$

Step-by-step explanation:

Given

$(x_1, y_1) = (1,12)$

$(x_2, y_2) = (0,3)$

Required

The function of the graph (exponential function)

An exponential function is represented as:

$f(x) = ab^x$

For $(x_1, y_1) = (1,12)$, we have:

$12 = a * b^1$

$12 = a * b$

$12 = a b$

For $(x_2, y_2) = (0,3)$

$3 = a * b^0$

$3 = a * 1$

$3 = a$

$a = 3$

Substitute: $a = 3$ in $12 = a b$

$12 = 3 * b$

Divide both sides by 3

$4 = b$

$b =4$

So, we have:

$f(x) = ab^x$

$f(x) =3 * (4)^x$