A cup of coffee has an initial temperature of when it is placed in a room whose air…

MATHEMATICS · Single correct · AP · Calculus AB · Differential Equations · Differential Equations

Problem

A cup of coffee has an initial temperature of

90^{\circ}\text{C}

when it is placed in a room whose air temperature is

20^{\circ}\text{C}

. Its temperature

T(t)

(in °C) obeys

\dfrac{dT}{dt}=k\,(T-20)

, where

t

is measured in minutes and

k

is a constant. After 10 minutes, the coffee’s temperature is

60^{\circ}\text{C}

. Which of the following is closest to the coffee’s temperature after a total of 20 minutes in the room? (a)

52^{\circ}\text{C}

(b)

35^{\circ}\text{C}

(c)

43^{\circ}\text{C}

(d)

40^{\circ}\text{C}