Answer:
1.09
Step-by-step explanation:
To find the dimension [tex] D [/tex] of a fractal with a scaling ratio [tex] r [/tex] and a replacement ratio [tex] N [/tex], we use the formula:
[tex] D = \dfrac{\log(N)}{\log(r)} [/tex]
Given:
- Scaling ratio [tex] r = 9 [/tex]
- Replacement ratio [tex] N = 11 [/tex]
We can substitute these values into the formula:
[tex] D = \dfrac{\log(11)}{\log(9)} [/tex]
Using a calculator, we find:
[tex] D \approx \dfrac{1.041392685}{0.9542425094} [/tex]
[tex] D \approx 1.0913291692012[/tex]
[tex] D \approx 1.09 \textsf{(in nearest hundredth)}[/tex]
Therefore, the dimension [tex] D [/tex] of the fractal is approximately 1.09.
