Mathematics

Problem

Two identical cups of coffee are initially

90^{\circ}\text{C}

and cool in a

22^{\circ}\text{C}

office. Cup A satisfies

\displaystyle \frac{dT}{dt}=k_A\,(T-22)

with

k_A=-0.05\,\text{min}^{-1}

, and Cup B satisfies the same form with

k_B=-0.08\,\text{min}^{-1}

. Which statement best describes their temperatures after

15

minutes? a) Cup A is about

42^{\circ}\text{C}

, while Cup B is about

54^{\circ}\text{C}

. b) Both cups are near

54^{\circ}\text{C}

. c) Cup A is about

54^{\circ}\text{C}

, while Cup B is about

42^{\circ}\text{C}

. d) After

15

minutes both cups are within

1^{\circ}\text{C}

22^{\circ}\text{C}