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?

Answer 1

Answer: 56

Given: c(x) + h(x) = temperature, find the value when x = 5

Step by Step: c(x) + h(x) =
`(0.5)^x^-^1^1` - x - 3

=
`(0.5)^5^-^1^1 - 5 - 3`

=
`(0.5)^-^6 - 8`

=
`(1)/(0.5^6) - 8`

=
`(1)/(0.15625) - 8`

=
`64 - 8`

= 56

Answer 2

The temperature of metal after five years = -18.96875

Explanation:

Given : Function
`c(x) = (0.5)^x-11`

where x is measured in hours

Another function is added h(x)=-x-3

therefore, the resultant function f(x)=h(x)+c(x)

`f(x) = (0.5)^x-11-x-3`

For x=5

`f(5) = (0.5)^5-11-5-3`

`f(5) = (0.03125)-19`

`f(5) = -18.96875`

Therefore, The temperature of metal after five years = -18.96875