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?
A. −8° Celsius

B. 26° Celsius

C. 32° Celsius

D. 56° Celsius

Answer 1

@phi I plugged 5 in where f(x) and h(x) were to get the equations
\[5=(.5)^{x-11} \] which came out to x=8.6780, and the equation
\[5=-x-3\] which came out to x=-8.
So is it A? I just want to make sure..

Answer 2

c(x) gives the temperature of the metal after cooling for x hours.

For example, at the very start , where we cool for no time, x=0, and we find
c(0)= (.5)^(− 11)= 2^11 = 2048 degrees
after 1 hour, the temperature is
c(1) = 0.5^-10 = 1024 degrees.

you want the temperature when x = 5 hours.

can you find c(5) ?

Answer 3

though they are not very clear, they say
A device is added that aids in cooling according to the function h(x) = −x − 3
For x= 5 hours, h(5) = -5 - 3 = -8
I assume this means the metal cools by another 8 degrees below c(5)

so find
c(5)
and then add -8 (or, subtract 8 degrees)
to get the final answer.