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? (1 point)

Answer 1

16.5 degrees below the starting temp, whatever that is. If its 0, then -16.5 degrees.

The first equation would be (.5)5-11=-8.5, because the metal has been cooling for 5 hours.

The device that 'aids' in the cooling would be -5-3=-8, because it is a separate variable that cools the metal, so the amount the device cools is independent of the natural cooling amount, and the equation is independent of the natural cooling equation.
You then add -8.5 and -8, because the device has lowered 8.5 degrees and 8 degrees. This equals -16.5 degrees, or a decrease of 16.5 degrees.