To find the revenue when 12 units are sold, we need to follow these steps:
1. Determine the unit price [tex]\( p(x) \)[/tex]:
The unit price is given by the function [tex]\( p(x) = 34 \times 3^{\frac{2}{4}} \)[/tex].
To simplify [tex]\( 3^{\frac{2}{4}} \)[/tex]:
[tex]\[
3^{\frac{2}{4}} = 3^{\frac{1}{2}} = \sqrt{3}
\][/tex]
The value of [tex]\( \sqrt{3} \)[/tex] is approximately 1.732.
So, the unit price [tex]\( p(x) \)[/tex] becomes:
[tex]\[
p(x) = 34 \times 1.732 \approx 58.89
\][/tex]
2. Calculate the revenue [tex]\( R(x) \)[/tex]:
The revenue [tex]\( R(x) \)[/tex] is calculated by multiplying the number of units sold [tex]\( x \)[/tex] by the unit price [tex]\( p(x) \)[/tex].
Given that [tex]\( x = 12 \)[/tex] units and [tex]\( p(x) \approx 58.89 \)[/tex]:
[tex]\[
R(x) = 12 \times 58.89 \approx 706.68
\][/tex]
3. Round the revenue to two decimal places:
The revenue to two decimal places is already [tex]\( \approx 706.68 \)[/tex].
Thus, if 12 units are sold, the revenue is approximately $706.68.
