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 Degrees Celsius
6 Degrees Celsius
9 Degrees Celsius
16 Degrees Celsius
To find the temperature of the metal after five hours, we need to evaluate the composite function c(h(5)).
First, let's find the value of h(5):
h(x) = -x - 2
h(5) = -(5) - 2
h(5) = -5 - 2
h(5) = -7
Next, let's substitute h(5) into the function c(x):
c(x) = (0.5)^(x - 9)
c(h(5)) = (0.5)^(-7 - 9)
c(h(5)) = (0.5)^(-16)
To calculate (0.5)^(-16), we can use the property that a negative exponent flips the number to its reciprocal:
(0.5)^(-16) = 1/(0.5)^16
Now let's calculate (0.5)^16:
(0.5)^16 = 0.0000000596
So, 1/(0.5)^16 = 1/0.0000000596 = 16,807,272.88
Therefore, the temperature of the metal after five hours will be approximately 16,807,272.88 degrees Celsius.
Therefore, the correct option is: 16 Degrees Celsius.