Question

A heated piece of metal cools according to the function c(x) = (.5)x − 9, 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 five hours? −7° Celsius 6° Celsius 9° Celsius 16° Celsius

Answer 1

9 degrees celsius, hope this helped!

Answer 2

9° Celsius

Explanation:

Given,

The heated piece of metal cools according to the function,

`C(x)=(0.5)^(x-9)`

After adding the device that cools according the function,

`h(x)=-x-2`

The new function that shows the final temperature of the metal,

`f(x)=C(x)+h(x)` ( Let )

`=(0.5)^(x-9)-x-2`

Hence, the temperature of the metal after five hours would be,

`f(3) = (0.5)^(5-9)-5-2 =0.5^(-4)-7=((1)/(2))^(-4)-7=2^4-7=16-7=9^(\circ)\text{ Celsius}`

Third Option is correct.