Answer :
To determine the profit we would earn from selling T-shirts at a price of [tex]$15 each, we need to substitute \( x = 15 \) into the profit function \( p(x) = -2(x-9)^2 + 100 \).
Here are the steps:
1. Start with the given profit function:
\[
p(x) = -2(x-9)^2 + 100
\]
2. Substitute \( x = 15 \) into the function:
\[
p(15) = -2(15-9)^2 + 100
\]
3. Calculate the expression inside the parentheses first:
\[
15 - 9 = 6
\]
4. Now square the result:
\[
6^2 = 36
\]
5. Multiply this squared result by \(-2\):
\[
-2 \times 36 = -72
\]
6. Finally, add 100 to -72 to find the profit:
\[
-72 + 100 = 28
\]
So, the profit when the T-shirts are sold for $[/tex]15 each would be \$28. Thus, the correct answer is:
[tex]\(\boxed{28}\)[/tex]
[tex]\(\boxed{28}\)[/tex]
