(a) Using Newton's Law of Cooling,
, we have
where T is temperature after T minutes.
Separate by dividing both sides by T - 75 to get
. Integrate both sides to get
.
Since
, we solve for C:
So we get
. Use T(30) = 150 to solve for k:
So
But choose Positive because T > 75. Temp of turkey can't go under.
(b)
Dogs of the AMS.
And whats the rest of the question
The answer is 2.6 because 2.6+2=4.6
This is a strange question, and f(x) may not even exist. Why do I say that? Well..
[1] We know that f(a+b) = f(a) + f(b). Therefore, f(0+0) = f(0) + f(0). In other words, f(0) = f(0) + f(0). Subtracting, we see, f(0) - f(0) = f(0) or 0 = f(0).
[2] So, what's the problem? We found the answer, f(0) = 0, right? Maybe, but the second rule says that f(x) is always positive. However, f(0) = 0 is not positive!
Since there is a contradiction, we must either conclude that the single value f(0) does not exist, or that the entire function f(x) does not exist.
To fix this, we could instead say that "f(x) is always nonnegative" and then we would be safe.
Answer:
the answer to that question is 12,600 rupees
