Question

question 5
for the function ( f(x)=8 e^{x} ), calculate the following function values:
( f(-3)=)
( f(-1)=)
( f(0)=)
( f(1)=)
( f(3)=)
question help: video

Explanation:

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

\(f(-3)=8e^{-3}=\frac{8}{e^{3}}\approx\frac{8}{20.0855}\approx0.398\)

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

\(f(-1)=8e^{-1}=\frac{8}{e}\approx\frac{8}{2.7183}\approx2.943\)

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

Since \(e^{0}=1\), then \(f(0)=8e^{0}=8\times1 = 8\)

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

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

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

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

Answer:

\(f(-3)\approx0.398\)
\(f(-1)\approx2.943\)
\(f(0)=8\)
\(f(1)\approx21.746\)
\(f(3)\approx160.684\)