Question

for the function $f(x)=7e^{x}$, calculate the following function values. round your answer to 6 decimal places.
$f(-3)=$
$f(-1)=$
$f(0)=$
$f(1)=$
$f(3)=$
question help: video

Explanation:

Step1: Substitute \(x = - 3\) into \(f(x)=7e^{x}\)

\(f(-3)=7e^{-3}\)
Using the property \(a^{-n}=\frac{1}{a^{n}}\), we have \(f(-3)=\frac{7}{e^{3}}\)
\(e\approx2.718282\), so \(e^{3}\approx20.085537\)
\(f(-3)=\frac{7}{20.085537}\approx0.348495\)

Step2: Substitute \(x = - 1\) into \(f(x)=7e^{x}\)

\(f(-1)=7e^{-1}=\frac{7}{e}\)
Since \(e\approx2.718282\), \(f(-1)=\frac{7}{2.718282}\approx2.575671\)

Step3: Substitute \(x = 0\) into \(f(x)=7e^{x}\)

\(f(0)=7e^{0}\)
Using the property \(a^{0}=1\) (\(a
eq0\)), we get \(f(0)=7\times1 = 7.000000\)

Step4: Substitute \(x = 1\) into \(f(x)=7e^{x}\)

\(f(1)=7e^{1}\)
Since \(e\approx2.718282\), \(f(1)=7\times2.718282\approx19.027974\)

Step5: Substitute \(x = 3\) into \(f(x)=7e^{x}\)

\(f(3)=7e^{3}\)
\(e^{3}\approx20.085537\), so \(f(3)=7\times20.085537\approx140.598759\)

Answer:

\(f(-3)\approx0.348495\)
\(f(-1)\approx2.575671\)
\(f(0)=7.000000\)
\(f(1)\approx19.027974\)
\(f(3)\approx140.598759\)