Question

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

Answer 1

Answer:

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

Step-by-step 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 $f(x) = 9 * (\frac13)^x$.