A turkey with a temperature of 40°F is moved to a 350°F oven. After 4 hours the internal temperature of the turkey is 170°F. If the turkey is done when its temperature reaches 185°F, then how much longer must it cook?
we have with , and
here is the temperature after time (in hours), is a constant, which we can find using and (as described in post #2 here, question 2), and is the ambient or surrounding temperature, in this case, the temperature of the oven
you want to find when , then you can answer the question
so we have
so now we want to know how long it takes for T to become 185, so we want t such that
now solve for . note that this gives the total time for the turkey to get to that temperature. you want the difference between 4 and that time