Question

question
if ( f(x)=7 e^{x} ), find which is the value of ( f(-3) ) rounded to the nearest hundredth.
select the correct answer below:
( \bigcirc 0.34 )
( \bigcirc 0.35 )
( \bigcirc 0.37 )
( \bigcirc 0.39 )
( \bigcirc 0.41 )

Explanation:

Step1: Substitute \(x = - 3\) into the function

Given \(f(x)=7e^{x}\), when \(x=-3\), we have \(f(-3)=7e^{-3}\).
Since \(a^{-n}=\frac{1}{a^{n}}\), then \(e^{-3}=\frac{1}{e^{3}}\), so \(f(-3)=\frac{7}{e^{3}}\).

Step2: Calculate the value

We know that \(e\approx2.71828\), then \(e^{3}\approx2.71828^{3}=20.0855\).
So \(f(-3)=\frac{7}{20.0855}\approx0.35\).

Answer:

0.35