Question

question
if ( f(x)=-9 e^{x} ), find which is the value of ( f(4) ) rounded to the nearest tenth.
select the correct answer below:
( -782.1 )
( -623.1 )
( -538.9 )
( -491.4 )
( -521.5 )

Explanation:

Step1: Substitute \(x = 4\) into the function

Given \(f(x)=-9e^{x}\), when \(x = 4\), we have \(f(4)=-9e^{4}\).

Step2: Calculate the value of \(e^{4}\)

We know that \(e\approx2.71828\), so \(e^{4}=(2.71828)^{4}\approx54.59815\).

Step3: Multiply by \(- 9\)

\(f(4)=-9\times54.59815=-491.38335\).

Step4: Round to the nearest tenth

Rounding \(-491.38335\) to the nearest tenth, we look at the hundredth digit. The hundredth digit is \(8\gt5\), so we round up the tenth digit. \(-491.38335\approx - 491.4\).

Answer:

\(-491.4\) (corresponding to the option \(-491.4\))