Mathematics

Problem

The temperature

T(t)\,\ (^{\circ}\text{C})

of a hot object in a room maintained at

30^{\circ}\text{C}

satisfies

\dfrac{dT}{dt}=-k\bigl(T-30\bigr)

, where

k>0

and

t

is in minutes. If

T(0)=90^{\circ}\text{C}

and

T(5)=70^{\circ}\text{C}

, find the temperature of the object after 15 minutes. a)

57^{\circ}\text{C}

(approximately) b)

48^{\circ}\text{C}

(approximately) c)

42^{\circ}\text{C}

(approximately) d)

58^{\circ}\text{C}

(approximately)