Question

Write an equation for the graph below.

Answer 1

Answer:

$f(x)= 3({2})^{x} - 3$

Step-by-step explanation:

Let the equation be of the form

$f(x)= a {b}^{x} + k$

be the equation, where k=-3 is the horizontal asymptote.

The equation now becomes:

$f(x)= a {b}^{x} - 3$The curve passes through (0,0)

$0= a {b}^{0} - 3$

$0 = a - 3$

a=3

This implies that:

$f(x)= 3{b}^{x} - 3$

We again substitute (1,3)

$3=3{b}^{1} - 3$

$3b = 6$

$b = 2$

The required equation is

$f(x)= 3({2})^{x} - 3$