Question

A roast turkey is taken from an oven when its temperature has reached 185°F and is placed on a table in a room where the temperature is 75°F. If the temperature of the turkey is 150°F after half an hour, what is the temperature after 35 minutes? Since the room temperature is 75°F, Newton's Law of Cooling says that dT/dt = k(T - 75). Separating this gives us 1 / (T - 75) dT = k dt. Integrating both sides gives us ln(T - 75) = kt + C, which becomes T = 75 + e^(kt + C). We now know that T = 75 + e^(kt + C) = 75 + Ke^(kt). Since T(0) = 185, then K = 110. We have T = 75 + 110e^(kt). Since the temperature after 30 minutes is 150°F, then e^(30k) = 15/22, and so k = 1/30 ln(15/22). Since T = 75 + 110e^((1/30) (ln(15/22)) t, we have the following. (Round your answer to the nearest whole number.) T(35) = °F When will the turkey have cooled to 95°F? We must solve 95 = 75 + 110e^((1/30) (ln(15/22)) t, or = e^((1/30) (ln(15/22)) t. Now, we have the following. (Round your final answer to the nearest whole number.) 1/30 (ln(15/22)) t = t = min

          A roast turkey is taken from an oven when its temperature has reached 185°F and is placed on a table in a room where the temperature is 75°F.
If the temperature of the turkey is 150°F after half an hour, what is the temperature after 35 minutes?
Since the room temperature is 75°F, Newton's Law of Cooling says that
dT/dt = k(T - 75).
Separating this gives us
1 / (T - 75) dT = k dt.
Integrating both sides gives us ln(T - 75) = kt + C, which becomes
T = 75 + e^(kt + C).
We now know that T = 75 + e^(kt + C) = 75 + Ke^(kt).
Since T(0) = 185, then K = 110.
We have T = 75 + 110e^(kt).
Since the temperature after 30 minutes is 150°F, then e^(30k) = 15/22, and so
k = 1/30 ln(15/22).
Since T = 75 + 110e^((1/30) (ln(15/22)) t, we have the following. (Round your answer to the nearest whole number.)
T(35) = °F
When will the turkey have cooled to 95°F?
We must solve 95 = 75 + 110e^((1/30) (ln(15/22)) t, or = e^((1/30) (ln(15/22)) t.
Now, we have the following. (Round your final answer to the nearest whole number.)
1/30 (ln(15/22)) t =
t = min

A roast turkey is taken from an oven when its temperature has reached 185°F and is placed on a table in a room where the temperature is 75°F.
If the temperature of the turkey is 150°F after half an hour, what is the temperature after 35 minutes?
Since the room temperature is 75°F, Newton's Law of Cooling says that
dT/dt = k(T - 75).
Separating this gives us
1 / (T - 75) dT = k dt.
Integrating both sides gives us ln(T - 75) = kt + C, which becomes
T = 75 + e^(kt + C).
We now know that T = 75 + e^(kt + C) = 75 + Ke^(kt).
Since T(0) = 185, then K = 110.
We have T = 75 + 110e^(kt).
Since the temperature after 30 minutes is 150°F, then e^(30k) = 15/22, and so
k = 1/30 ln(15/22).
Since T = 75 + 110e^((1/30) (ln(15/22)) t, we have the following. (Round your answer to the nearest whole number.)
T(35) = °F
When will the turkey have cooled to 95°F?
We must solve 95 = 75 + 110e^((1/30) (ln(15/22)) t, or = e^((1/30) (ln(15/22)) t.
Now, we have the following. (Round your final answer to the nearest whole number.)
1/30 (ln(15/22)) t =
t = min

Added by Beverly E.

Question

Please give Ace some feedback