Question

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 5 hours?
−7° Celsius
6° Celsius
9° Celsius
16° Celsius

Answer 1

Answer:

9° Celsius option C.

Step-by-step explanation:

Heated piece of metal cools according to the function

$c(x)=(0.5)^{(x-9)}$

Now a device has been added that aids in cooling the metal according to the function.

h(x) = (-x -2)

Then temperature of the metal after x hours will be

g(x) = c(x) + h (x)

      = $(0.5)^{(x-9)}-x-2$

At x = 5  g (5) = $(0.5)^{(5-9)}-5-2$

= $(0.5)^{-4}-7$

= $\frac{1}{(0.5)^{4}}-7$

= 16 - 7

= 9° Celsius

Option C is the answer.

Answer 2

In both cases, we have cooling.  We can add together the 2 functions describing this cooling:  z(x) = 0.5x - 9 - [-x-2] = 0.5x - 9 + x + 2, or

z(x) = 1.5x - 7

Provided that this is correct, all we have to do now is to subst. 5 for x:

z(5) = 1.5(5) - 7 = 7.5 - 7 = 0.5 (answer)