Question

for the function $f(x)=8e^{x}$, calculate the following function values: round your answer to three decimal places.
$f(-3)=$
$f(-1)=$
$f(0)=$
$f(1)=$
$f(3)=$

Explanation:

Step1: Substitute \(x = - 3\) into \(f(x)=8e^{x}\)

\(f(-3)=8e^{-3}=8\times\frac{1}{e^{3}}\approx8\times0.0498 = 0.398\)

Step2: Substitute \(x=-1\) into \(f(x)=8e^{x}\)

\(f(-1)=8e^{-1}=8\times\frac{1}{e}\approx8\times0.3679 = 2.943\)

Step3: Substitute \(x = 0\) into \(f(x)=8e^{x}\)

\(f(0)=8e^{0}=8\times1=8.000\)

Step4: Substitute \(x = 1\) into \(f(x)=8e^{x}\)

\(f(1)=8e^{1}=8\times e\approx8\times2.7183 = 21.746\)

Step5: Substitute \(x = 3\) into \(f(x)=8e^{x}\)

\(f(3)=8e^{3}\approx8\times20.0855 = 160.684\)

Answer:

\(f(-3)=0.398\)
\(f(-1)=2.943\)
\(f(0)=8.000\)
\(f(1)=21.746\)
\(f(3)=160.684\)