Newton's Law of Cooling States That the Rate of Cooling $160 ^ { \circ } \mathrm { F }$

Multiple Choice

Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. Suppose that a roast turkey is taken from an oven when its temperature has reached $160 ^ { \circ } \mathrm { F }$ and is placed on a table in a room where the temperature is $60 ^ { \circ } \mathrm { F }$ . If $u ( t )$ is the temperature of the turkey after $t$ minutes, then Newton's Law of Cooling implies that $\frac { d u } { d t } = k ( u - 60 ) \text {. }$ This could be solved as a separable differential equation. Another method is to make the change of variable $y = u - 60$ . If the temperature of the turkey is $150 ^ { \circ } \mathrm { F }$ after half an hour, what is the temperature after $35 \mathrm {~min}$ ?

A) $t = 143 ^ { \circ } \mathrm { F }$
B) $t = 148 ^ { \circ } \mathrm { F }$
C) $t = 298 ^ { \circ } \mathrm { F }$
D) none of these
E) $t = 95 ^ { \circ } \mathrm { F }$