Sure! Let's simplify the base for the function [tex]\( f(x) = 2 \left( \frac{3}{272} \right)^x \)[/tex].
1. First, look at the fraction inside the parentheses: [tex]\(\frac{3}{272}\)[/tex].
2. Evaluate the fraction: [tex]\(\frac{3}{272}\)[/tex]. When you divide 3 by 272, you get approximately [tex]\(0.011029411764705883\)[/tex].
So, the simplified base of the function [tex]\( f(x) = 2 \left( \frac{3}{272} \right)^x \)[/tex] is approximately [tex]\( 0.011029411764705883 \)[/tex].
Among the given choices:
- 2
- 3
- 9
- 18
None of these choices match our simplified base value ([tex]\( \approx 0.011029411764705883 \)[/tex]).
Therefore, we can deduce that none of the given options are the correct simplified base. If you seek a more simplified or approximated answer, it might be nearest to 1% or [tex]\( \sim 0.01 \)[/tex].
