To solve the problem [tex]\( n(t) = -2(t + 5)^2 + 4 \)[/tex] and find [tex]\( n(-8) \)[/tex], follow these steps:
1. Start with the given function:
[tex]\[
n(t) = -2(t + 5)^2 + 4
\][/tex]
2. Substitute [tex]\( t \)[/tex] with [tex]\( -8 \)[/tex]:
[tex]\[
n(-8) = -2((-8) + 5)^2 + 4
\][/tex]
3. Simplify the expression inside the parentheses:
[tex]\[
-8 + 5 = -3
\][/tex]
So the expression now becomes:
[tex]\[
n(-8) = -2(-3)^2 + 4
\][/tex]
4. Calculate the square of [tex]\(-3\)[/tex]:
[tex]\[
(-3)^2 = 9
\][/tex]
So the expression simplifies to:
[tex]\[
n(-8) = -2 \times 9 + 4
\][/tex]
5. Perform the multiplication:
[tex]\[
-2 \times 9 = -18
\][/tex]
Now the expression is:
[tex]\[
n(-8) = -18 + 4
\][/tex]
6. Finally, add [tex]\( -18 \)[/tex] and [tex]\( 4 \)[/tex]:
[tex]\[
-18 + 4 = -14
\][/tex]
Hence, the value of [tex]\( n(-8) \)[/tex] is:
[tex]\[
n(-8) = -14
\][/tex]
Therefore, the correct answer from the given options is:
[tex]\[
-14
\][/tex]
