(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.
First remove parenthesis. Next collect the like terms. Next move terms. Next collect the like terms and calculate. Divide both sides by 8. Your answer is -2