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A heated piece of metal cools according to the function c(x) = (.5)^(x _ 11), where x is measured in hours. A device is added that aids in cooling according to the function h(x) = _x _ 3. What will be the temperature of the metal after five hours?

A_8Á Celsius

B26Á Celsius

C32Á Celsius

D56Á Celsius

Verified Answer :

You just need to replace x with 5 in each function

.5^5 - 11
-5-3

.5 ^-6
-8


64 - 8 = 56 A Celcius

Hope this helps

Answer:

Option D

Explanation:

A heated piece of metal cools according to the function \(c(x) = (0.5)^{x-11}\)

And a device which aids in cooling is added is represented by the function h(x) = -x - 3

Temperature of the metal after x hours will be represented by

c(x) + h(x) = \((0.5)^{x-11}+(-x-3)\)

               = \((0.5)^{x-11}-x-3\)

We have to find the temperature after 5 hours

So c(5) - h(5) = \((0.5)^{5-11}-5-3\)

                     = \((0.5)^{-6}-8\)

                     = 64 - 8

                     = 56° Celsius

Option D is the answer.

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