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?

Answer 1

Answer: -10.75 Celsius

Explanation:

Here, A heated piece of metal cools according to the function,

`c(x) = (.5)^x-7`

Where x represents the number of hours.

Again according to the question, A device is added that aids in cooling according to the function h(x) = -x - 2.

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

Thus,
`f(x)=(.5)^x - 7 - x- 2`

⇒
`f(x)=(.5)^x - x -9`, where x is the number of hours.

After two hours, x=2

`f(2)= (.5)^2 - 2 -9`

⇒
`f(2)= (.5)^2 - 11`

⇒f(2)= -10.75 Celsius