Which of the following expresses the temperature of a cooling body at time in terms…

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

Problem

Which of the following expresses the temperature

T(t)

of a cooling body at time

t

in terms of its ambient temperature

T_s

, initial temperature

T_0

, and cooling constant

k

? (a)

T(t)=T_s+(T_0-T_s)e^{kt}

(b)

T(t)=T_s+T_0 e^{-kt}

(c)

T(t)=T_s+(T_0-T_s)e^{-kt}

(d)

T(t)=T_0 e^{-kt}