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