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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 :

shyniyahsills

9 degrees celsius, hope this helped!

Answer:

9° Celsius

Step-by-step explanation:

Given,

The heated piece of metal cools according to the function,

[tex]C(x)=(0.5)^{x-9}[/tex]

After adding the device that cools according the function,

[tex]h(x)=-x-2[/tex]

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

[tex]f(x)=C(x)+h(x)[/tex]  ( Let )

[tex]=(0.5)^{x-9}-x-2[/tex]

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

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

Third Option is correct.

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