Question

A heated piece of metal cools according to the function c(x) = (.5)x − 7, 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 two hours?

−4° Celsius
28° Celsius
32° Celsius
38° Celsius

Answer 1

since you are not told the starting temperatutre you cannot answer this

Answer 2

right

Answer 3

hmmm - I may be wrong above. The question seems incorrect BUT it doesnt actually include any reference to the starting temperatiure.

if you set t=0 then the initial condtion is c(0) = -7

however then c(1) = -6.5 whicvh is not a 'cooling'

Have you written this properly?
should it be
\[c(x) = (0.5)^{x} -7\]

this woulf be more likely since it is an exponential

Please ensure you have written the functions properly
Use the Draw option if you can't use teh equation editor

Answer 4

@mrnood @welshfella
I apologize! the function is \[c(x)=(.5)^{x-7}\]

Answer 5

@pooja195 @wolf1728 @agent0smith

Answer 6

Using the formula (.5^(x-7), I obtained these numbers:
Hours Temp
12.00 0.03
11.00 0.06
10.00 0.13
9.00 0.25
8.00 0.50
7.00 1.00
6.00 2.00
5.00 4.00
4.00 8.00
3.00 16.00
2.80 18.38
2.60 21.11
2.40 24.25
2.20 27.86
2.00 32.00