Question

A heated piece of metal cools according to the function c(x) = (.5)x − 7, where x is measured in hours. a device is added that aids in cooling according to the function h(x) = −x − 2. what will be the temperature of the metal after 2 hours?

Answer 1

c(x) = (.5)x – 7

h(x) = −x – 2

c(h(x)) = (.5)( −x – 2) – 7


           = -0.5x - 1 – 7


c(h(x))     = -0.5x – 8

Temperature after 2 hours:

Put x = 2

c(h(x))     = -0.5(2) – 8

              = -1 – 8
              = -9

Answer 2

Answer:

Temperature = -10.75 degree  

Step-by-step explanation:

Given : A heated piece of metal cools according to the function $c(x) = (0.5)^x-7$ 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 two hours.

Solution : $c(x) = (0.5)^x-7$   and  $h(x) = -x-2$

First we find the total device or function used to cool the heated piece f(x)

$f(x)=c(x)+h(x)$

$f(x)= (0.5)^x-7+(-x-2)$

$f(x)= (0.5)^x-7-x-2$

Temperature of metal after five hours ⇒ x=2

$f(x)= (0.5)^2-7-2-2$

$f(x)= 0.25-11$

$f(x)= -10.75$

Therefore, temperature = -10.75 degree