Question

You place a cup of 205oF coffee on a table in a room that is 72oF, and 10 minutes later, it is 195oF. Approximately how long will it be before the coffee is 180oF? Use Newton's law of cooling:
A. 1 hour
B. 25 minutes
C. 45 minutes
D. 15 minutes

Answer 1

work always with the differences between the heated coffee and the room temp
first number we need is \(205-72=133\)

Answer 2

second number is \(195-72=123\)

Answer 3

this takes 10 minutes to occur, so you can model this as \[133\left(\frac{123}{133}\right)^{\frac{t}{10}}\]

Answer 4

since \(180-72=108\) set
\[108=133\left(\frac{123}{133}\right)^{\frac{t}{10}}\] and solve for
(t\)