let ( h(w)=-4 e^{w + 3} ) evaluate the following expressions. use a calculator, when necessary. round…

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)= )

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)= )

Answer

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 )