Answer:
[tex]f(x) = 9 * (\frac13)^x[/tex]
Step-by-step explanation:
Hello!
Let's break down the formula [tex]f(x) = a*b^x[/tex]
- [tex]a = \text{starting value, when x = 0}[/tex]
- [tex]b = \text{multiplier}[/tex]
- [tex]x = \text{Number of times multiplied}[/tex]
Looking at the graph, we can see that [tex]a = 9[/tex], as it is when x is 0, and is the starting point.
To solve for the multiplier ([tex]b[/tex]):
- 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:
- [tex]f(x) = a*b^x[/tex]
- [tex]a = 9, b = \frac13[/tex]
- [tex]f(x) = 9 * (\frac13)^x[/tex]
The equation in [tex]f(x) = a*b^x[/tex] form is [tex]f(x) = 9 * (\frac13)^x[/tex].
