Question

for the function $f(x)=4e^{x}$, calculate the following function values:
$f(-3)=$ enter your answer (round to 5 decimal places)
$f(-1)=$ enter your answer (round to 5 decimal places)
$f(0)=$ enter your answer (round to 5 decimal places)
$f(1)=$ enter your answer (round to 5 decimal places)
$f(3)=$ enter your answer (round to 5 decimal places)

Explanation:

Step1: Calculate \(f(-3)\)

Substitute \(x = - 3\) into \(f(x)=4e^{x}\), we get \(f(-3)=4e^{-3}\).
Using the formula \(a^{-n}=\frac{1}{a^{n}}\), so \(f(-3)=\frac{4}{e^{3}}\).
Since \(e\approx2.71828\), then \(e^{3}\approx20.08554\), and \(f(-3)=\frac{4}{20.08554}\approx0.19915\).

Step2: Calculate \(f(-1)\)

Substitute \(x=-1\) into \(f(x) = 4e^{x}\), we get \(f(-1)=4e^{-1}=\frac{4}{e}\).
Since \(e\approx2.71828\), then \(f(-1)=\frac{4}{2.71828}\approx1.47152\).

Step3: Calculate \(f(0)\)

Substitute \(x = 0\) into \(f(x)=4e^{x}\), we get \(f(0)=4e^{0}\).
Since \(e^{0}=1\), then \(f(0)=4\times1 = 4\).

Step4: Calculate \(f(1)\)

Substitute \(x = 1\) into \(f(x)=4e^{x}\), we get \(f(1)=4e^{1}\).
Since \(e\approx2.71828\), then \(f(1)=4\times2.71828 = 10.87312\).

Step5: Calculate \(f(3)\)

Substitute \(x = 3\) into \(f(x)=4e^{x}\), we get \(f(3)=4e^{3}\).
Since \(e^{3}\approx20.08554\), then \(f(3)=4\times20.08554=80.34216\).

Answer:

\(f(-3)\approx0.19915\)
\(f(-1)\approx1.47152\)
\(f(0)=4\)
\(f(1)\approx10.87312\)
\(f(3)\approx80.34216\)