Using Newton's cooling model, what will the temperature of a cup of hot tea be 2 hours after it is poured if its initial temperature is 200°F, the surrounding temperature is 70°F, and the value for k is 0.6?

A. 130

B. 109.16

C. 109.76

D. 71.35

E. 60

Question

Mathematics

Ethen

11 March, 01:33

Using Newton's cooling model, what will the temperature of a cup of hot tea be 2 hours after it is poured if its initial temperature is 200°F, the surrounding temperature is 70°F, and the value for k is 0.6?

A. 130

B. 109.16

C. 109.76

D. 71.35

E. 60

+2

Answers (1)

Know the Answer?

Jamison Hoover · Answer 1

Newton's Law of cooling is a differential equation that is simplified by using limits in temperature and time. The simplified equation is:

ln (T-Ts) = ln (T0-Ts) - kt

where

T is the final temperature

T0 is the initial temperature

Ts is the temperature of the surroundings

t is the time

k is a constant

Substituting the values:

ln (T-70) = ln (200-70) - (0.6) (2)

T = 109.16°F

The answer is B.

Using Newton's cooling model, what will the temperature of a cup of hot tea be 2 hours after it is poured if its initial temperature is 200°F, the surrounding temperature is 70°F, and the value for k is 0.6?A. 130B. 109.16C. 109.76D. 71.35E. 60

Using Newton's cooling model, what will the temperature of a cup of hot tea be 2 hours after it is poured if its initial temperature is 200°F, the surrounding temperature is 70°F, and the value for k is 0.6?

A. 130

B. 109.16

C. 109.76

D. 71.35

E. 60