To solve for the values of the function [tex]\( f(x) = 8e^x \)[/tex] at specific points, we will substitute each given value of [tex]\( x \)[/tex] into the function and compute the result.
1. Calculating [tex]\( f(-3) \)[/tex]:
[tex]\[
f(-3) = 8e^{-3}
\][/tex]
When computed, [tex]\( 8e^{-3} \)[/tex] approximately equals:
[tex]\[
f(-3) \approx 0.39829654694291156
\][/tex]
2. Calculating [tex]\( f(-1) \)[/tex]:
[tex]\[
f(-1) = 8e^{-1}
\][/tex]
When computed, [tex]\( 8e^{-1} \)[/tex] approximately equals:
[tex]\[
f(-1) \approx 2.9430355293715387
\][/tex]
3. Calculating [tex]\( f(0) \)[/tex]:
[tex]\[
f(0) = 8e^{0}
\][/tex]
Since [tex]\( e^0 = 1 \)[/tex], we have:
[tex]\[
f(0) = 8 \cdot 1 = 8
\][/tex]
4. Calculating [tex]\( f(1) \)[/tex]:
[tex]\[
f(1) = 8e^{1}
\][/tex]
When computed, [tex]\( 8e^{1} \)[/tex] approximately equals:
[tex]\[
f(1) \approx 21.74625462767236
\][/tex]
5. Calculating [tex]\( f(3) \)[/tex]:
[tex]\[
f(3) = 8e^{3}
\][/tex]
When computed, [tex]\( 8e^{3} \)[/tex] approximately equals:
[tex]\[
f(3) \approx 160.68429538550134
\][/tex]
Therefore, the values of the function [tex]\( f(x) = 8e^x \)[/tex] at the specified points are:
[tex]\[
\begin{array}{l}
f(-3) \approx 0.39829654694291156 \\
f(-1) \approx 2.9430355293715387 \\
f(0) = 8 \\
f(1) \approx 21.74625462767236 \\
f(3) \approx 160.68429538550134
\end{array}
\][/tex]
