Answer:
Option (b) is correct.
The temperature of the metal after two hours is 28 Celsius
Step-by-step explanation:
Given : A heated piece of metal cools according to the function
, where x is measured in hours and then a cooling device id added that aids in cooling according to the function ![h(x)=-x-2](https://tex.z-dn.net/?f=h%28x%29%3D-x-2)
We have to determine the temperature of the metal after two hours.
Let w(x) denotes the temperature of metal .
Thus, w(x) can be given by function c(x) + h (x) = [c + h](x)
Thus,
, where x is measured in hours.
Thus, after two hours that is when x = 2
the temperature of metal is given by w(2)
![w(x)=(0.5)^{x-7}+(-x-2)\\\\ w(2)=(0.5)^{2-7}+(-2-2)](https://tex.z-dn.net/?f=w%28x%29%3D%280.5%29%5E%7Bx-7%7D%2B%28-x-2%29%5C%5C%5C%5C%20w%282%29%3D%280.5%29%5E%7B2-7%7D%2B%28-2-2%29)
Solving , we get,
![w(2)=(0.5)^{2-7}+(-2-2)\\\\ w(2)=(0.5)^{-5}+(-4)\\\\ w(2)=32-4=28](https://tex.z-dn.net/?f=w%282%29%3D%280.5%29%5E%7B2-7%7D%2B%28-2-2%29%5C%5C%5C%5C%20w%282%29%3D%280.5%29%5E%7B-5%7D%2B%28-4%29%5C%5C%5C%5C%20w%282%29%3D32-4%3D28)
Thus, the temperature of the metal after two hours is 28 Celsius.
Hence, Option (b) is correct.