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

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

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

= $\frac{1}{0.5^6} - 8$

= $\frac{1}{0.15625} - 8$

= $64 - 8$

= 56

Answer 2

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