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

question 103

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
$$\frac { d u } { d t } = k ( u - 60 )$$
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) \(t = 95 ^ { \circ } \mathrm { F }\)

---

Definitions:

Night-Fragranced

Refers to plants or substances that release their aroma primarily during the evening or night time.

Large

Describes something of significant size or extent, often exceeding what is common or usual.

Pollinator

An organism that moves pollen from the male anthers of a flower to the female stigma of a flower to accomplish fertilization, including bees, butterflies, and birds.

Hypertension

A chronic medical condition characterized by consistently high blood pressure, which can lead to serious health problems such as heart disease and stroke.