The temperature (in C) of a liquid is modeled for minutes by the differential…

MATHEMATICS · Multi-part · IB Diploma Programme · Mathematics: Applications and Interpretation · Calculus · Calculus

Problem

The temperature

T

(in

^{\circ}

C) of a liquid is modeled for

t\ge0

minutes by the differential equation

T''(t)=e^{0.2t}-0.5.

At the instant heating begins, the liquid is at rest so that

T'(0)=0

, and its initial temperature is

25^{\circ}

C. (a) Determine the liquid’s rate of change of temperature

T'(t)

. (b) Determine the temperature function

T(t)

. (c) Using your expression from part (b), estimate (to two decimal places) the time at which the liquid first reaches

30^{\circ}