To determine the profit from T-shirt sales when the price per T-shirt is [tex]$15, we need to evaluate the profit function \( p(x) = -2(x - 9)^2 + 100 \) at \( x = 15 \).
Let's break down the process step-by-step:
1. Substitute \( x = 15 \) into the profit function \( p(x) \):
\[
p(15) = -2(15 - 9)^2 + 100
\]
2. Calculate the expression inside the parentheses:
\[
15 - 9 = 6
\]
3. Square the result:
\[
6^2 = 36
\]
4. Multiply by \(-2\):
\[
-2 \times 36 = -72
\]
5. Add 100 to the result:
\[
-72 + 100 = 28
\]
So, the profit from sales when the T-shirts are priced at $[/tex]15 apiece is [tex]\(\$28\)[/tex].
Thus, the correct answer is:
[tex]\(\$ 28\)[/tex]
