A laboratory sample obeys with constant

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

A laboratory sample obeys

\displaystyle \frac{dT}{dt}=k\,(T-18)

with constant

k

. Which conclusion about

k

is most consistent with the fact that the sample’s temperature decreases toward

18^{\circ}\text{C}

over time? (a)

k>0

, and a larger value of

k

produces slower cooling. (b)

k<0

, and a larger

|k|

produces faster cooling. (c)

k<0

, and a larger

|k|

produces slower cooling. (d)

k<0

, and a smaller

|k|

produces faster cooling.