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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

User Knyphe
by
8.7k points

2 Answers

1 vote

Answer:

Option B is correct.

28 Celsius

Explanation:

As per the statement:

A heated piece of metal cools according to the function


c(x) = (0.5)^(x-7) where x is measured in hours.

It is also given that:

A device is added that aids in cooling according to the function h(x) = −x − 2.

then the resultant metal of function becomes:


f(x) = c(x)+h(x)

Substitute the functions:


f(x) = (0.5)^(x-7) +(-x-2) ......[1]

We have to find the temperature of the metal after two hours.

⇒x =2 hours

Substitute the value in [1] we have;


f(2) = (0.5)^(2-7) +(-2-2)


f(2) = (0.5)^(-5) +(-4)


f(2) = 32 -4 = 28

Therefore, the temperature of the metal after two hours will be 28 Celsius

User Stanley Stuart
by
7.7k points
3 votes

Answer:

Option (b) is correct.

The temperature of the metal after two hours is 28 Celsius

Explanation:

Given : A heated piece of metal cools according to the function
c(x)=(0.5)^(x-7) , where x is measured in hours and then a cooling device id added that aids in cooling according to the function
h(x)=-x-2

We have to determine the temperature of the metal after two hours.

Let w(x) denotes the temperature of metal .

Thus, w(x) can be given by function c(x) + h (x) = [c + h](x)

Thus,
w(x)=[c+h](x)\\\\w(x)=(0.5)^(x-7)+(-x-2)\\\\ , where x is measured in hours.

Thus, after two hours that is when x = 2

the temperature of metal is given by w(2)


w(x)=(0.5)^(x-7)+(-x-2)\\\\ w(2)=(0.5)^(2-7)+(-2-2)

Solving , we get,


w(2)=(0.5)^(2-7)+(-2-2)\\\\ w(2)=(0.5)^(-5)+(-4)\\\\ w(2)=32-4=28

Thus, the temperature of the metal after two hours is 28 Celsius.

Hence, Option (b) is correct.

User Rob Deary
by
8.0k points
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