A cup of tea is initially and cools to in minutes in a room

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

Problem

A cup of tea is initially

90^{\circ}\text{C}

and cools to

60^{\circ}\text{C}

5

minutes in a

25^{\circ}\text{C}

room. Assuming the tea continues to cool according to

\displaystyle \frac{dT}{dt}=k\,(T-25)

with the same constant

k

, approximately how many minutes after it was first poured will the tea reach

40^{\circ}\text{C}

? (a)

10\text{ minutes}

(b)

8\text{ minutes}

(c)

12\text{ minutes}

(d)

9\text{ minutes}