Question

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

B. 26Á Celsius

C. 32Á Celsius

D. 56Á Celsius

Answer 1

Option D

Step-by-step 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.

Answer 2

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