Question

Write the function of the graph in f(x) = a • bx form

Answer 1

`f(x) = 9 * (\frac13)^x`

Explanation:

Hello!

Let's break down the formula
`f(x) = a*b^x`

• 
  `a = \text{starting value, when x = 0}`
• 
  `b = \text{multiplier}`
• 
  `x = \text{Number of times multiplied}`

Looking at the graph, we can see that
`a = 9`, as it is when x is 0, and is the starting point.

To solve for the multiplier (
`b`):

• divide the next term by the prevoius term

Multiplier:

• When x = 0, the value is 9
• When x = 1, the value is 3
• 3/9 = 1/3
• The multipler is 1/3

So, plug in the values:

• 
  `f(x) = a*b^x`
• 
  `a = 9, b = \frac13`
• 
  `f(x) = 9 * (\frac13)^x`

The equation in
`f(x) = a*b^x` form is
`f(x) = 9 * (\frac13)^x`.