Question

let ( h(w)=-4 e^{w + 3} ) evaluate the following expressions. use a calculator, when necessary. round solutions to four decimal places, if necessary. ( h(1)= ) enter an integer or decimal number more.. ( h(4)= ) ( h(-3)= ) ( h(0)= )

Explanation:

Step1: Substitute \( w = 1 \) into \( h(w) \)

\( h(1)=-4e^{1 + 3}=-4e^{4} \). Using a calculator, \( e^{4}\approx54.5982 \), so \( h(1)=-4\times54.5982=-218.3928 \)

Step2: Substitute \( w = 4 \) into \( h(w) \)

\( h(4)=-4e^{4 + 3}=-4e^{7} \). Using a calculator, \( e^{7}\approx1096.6332 \), so \( h(4)=-4\times1096.6332=-4386.5328 \)

Step3: Substitute \( w=-3 \) into \( h(w) \)

\( h(-3)=-4e^{-3 + 3}=-4e^{0} \). Since \( e^{0}=1 \), then \( h(-3)=-4\times1=-4 \)

Step4: Substitute \( w = 0 \) into \( h(w) \)

\( h(0)=-4e^{0+ 3}=-4e^{3} \). Using a calculator, \( e^{3}\approx20.0855 \), so \( h(0)=-4\times20.0855=-80.3420 \)

Answer:

\( h(1)=-218.3928 \)
\( h(4)=-4386.5328 \)
\( h(-3)=-4 \)
\( h(0)=-80.3420 \)