Question

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Answer 1

The metal cools according to two different cooling functions, c(x) and h(x).
Combine these two functions into one. Then let x=2 (hours).

Answer 2

@mathmale ?

Answer 3

Let C(x) be the combined cooling function. Then C(x)=c(x)+h(x).

Please write C(x) here:

Answer 4

c(x) and h(x) are given in the problem statement. Just copy them into C(x)=c(x)+h(x).

Answer 5

I'd prefer to see the following, with a label:

C(x)=(.5)^x - 7 - x - 2 (which combines c(x) and h(x) ).

Please combine like terms in this expression.

C(x) = ??

Answer 6

C(x)=(.5)^x - 7 - x - 2 => C(x) = (.5)^7 - x - ( ? )

Answer 7

-7 - 2 = ???

Answer 8

My apologies. Here's the corrected form of the equation:

Then, C(x) = (.5)^x - x - 9 = (.5)^x - x - 9
Now, evaluate this function at x = 2.

Answer 9

Then C(2) = (.5)^2 - ( ? ) - 9 = ??

Answer 10

Your C(x) = (.5)^7 - 11 is incorrect because of my mistake: That's (.5)^2, not (.5)^7.

Answer 11

No; according to the original problem statement, we're interested in calculating the temperature at time t = 2.

Answer 12

Ah, ok, so its C(x) = (.5)^2 - 11?

Answer 13

How can I determine the temperature from here?

Answer 14

Simply substitute 2 for x in the formula given above. That 2 will represent the time "initial two hours of cooling."

Answer 15

Oh so substituting 2 into it, then the temperature is -4?

Answer 16

Once more:
C(x) = (.5)^x - x - 9
Therefore,
C(2) = (.5)^2 - 2 - 9 = 1/4 - 11

Answer 17

If C(x) = (.5)^2 - x - 9, then C(2) = (.5)^2 - 11 = (1/4)-11. Can you agree with this?

Note that .5 = 1/2, so (.5)^2 = (1/2)^2 = 1/4.

Answer 18

Let me know if any part of this is unclear; I'd be happy to discuss it further.

Answer 19

My great pleasure! Take care.