Question

Write an equation for the graph below.

Answer 1

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

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`