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 two hours?
-4 celsius
28 celsius
32 celsius
38 celsius

Answer 1

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  $c(x)=(0.5)^{x-7}$ ,  where x is measured in hours and then a cooling device id added that aids in cooling according to the function $h(x)=-x-2$

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, $w(x)=[c+h](x)\\\\w(x)=(0.5)^{x-7}+(-x-2)$ , where x is measured in hours.

Thus, after two hours that is when x = 2

the temperature of metal is given by w(2)

$w(x)=(0.5)^{x-7}+(-x-2)\\\\ w(2)=(0.5)^{2-7}+(-2-2)$

Solving , we get,

$w(2)=(0.5)^{2-7}+(-2-2)\\\\ w(2)=(0.5)^{-5}+(-4)\\\\ w(2)=32-4=28$

Thus, the temperature of the metal after two hours is 28 Celsius.

Hence, Option (b) is correct.

Answer 2

Answer:

Option B is correct.

28 Celsius

Step-by-step explanation:

As per the statement:

A heated piece of metal cools according to the function

$c(x) = (0.5)^{x-7}$ where x is measured in hours.

It is also given that:

A device is added that aids in cooling according to the function h(x) = −x − 2.

then the resultant metal of function becomes:

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

Substitute the functions:

$f(x) = (0.5)^{x-7} +(-x-2)$                    ......[1]

We have to find the temperature of the metal after two hours.

⇒x =2 hours

Substitute the value in [1] we have;

$f(2) = (0.5)^{2-7} +(-2-2)$

$f(2) = (0.5)^{-5} +(-4)$

⇒ $f(2) = 32 -4 = 28$

Therefore, the temperature of the metal after two hours will be 28 Celsius