To find the value of [tex]\( p(t) \)[/tex] at [tex]\( t = 2 \)[/tex], we need to substitute [tex]\( t = 2 \)[/tex] into the function [tex]\( p(t) = -3 |t + 1| \)[/tex] and evaluate it step by step.
1. Start with the given function:
[tex]\[
p(t) = -3 |t + 1|
\][/tex]
2. Substitute [tex]\( t = 2 \)[/tex] into the function:
[tex]\[
p(2) = -3 |2 + 1|
\][/tex]
3. Simplify the expression inside the absolute value:
[tex]\[
p(2) = -3 |3|
\][/tex]
4. Evaluate the absolute value:
[tex]\[
|3| = 3
\][/tex]
5. Finally, multiply by [tex]\(-3\)[/tex]:
[tex]\[
p(2) = -3 \times 3 = -9
\][/tex]
Thus, the value of [tex]\( p(2) \)[/tex] is [tex]\(\boxed{-9}\)[/tex].
