Answer:
Temperature = -15.96 degree
Step-by-step explanation:
Given : A heated piece of metal cools according to the function[tex]c(x) = (0.5)^x-9[/tex] where, x is measured in hours.
A device is added that aids in cooling according to the function [tex]h(x) = -x-2[/tex].
To find : The temperature of the metal after five hours.
Solution : [tex]c(x) = (0.5)^x-9[/tex] and [tex]h(x) = -x-2[/tex]
First we find the total device or function used to cool the heated piece f(x)
[tex]f(x)=c(x)+h(x)[/tex]
[tex]f(x)= (0.5)^x-9+(-x-2)[/tex]
[tex]f(x)= (0.5)^x-9-x-2[/tex]
Temperature of metal after five hours ⇒ x=5
[tex]f(5)= (0.5)^5-9-5-2[/tex]
[tex]f(5)= 0.03125-16[/tex]
[tex]f(5)=-15.96[/tex]
Therefore, temperature = -15.96 degree
