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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?

Verified Answer :

Answer:

The temperature of metal after five years =  -18.96875

Step-by-step 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

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

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

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

= \(\frac{1}{0.5^6} - 8\)

= \(\frac{1}{0.15625} - 8\)

= \(64 - 8\)

= 56

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