During a laboratory experiment

MATHEMATICS · Multi-part · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

During a laboratory experiment, the temperature

T(t)

(in

^{\circ}\text{C}

) of a solution is observed to follow the piece-wise description

T(t)=\begin{cases} 20+kt, & 0\le t<2,\\ 30+(t-2)^2, & 2\le t\le 5, \end{cases}

where

t

is the time in hours and

k

is a constant. (a) Determine the value of

k

that makes the temperature change without any sudden jump at

t=2

hours. (b) Using the value of

k

found in part (a), calculate the temperature of the solution at

t=2.5

hours.