A metal cube is heated to a temperature of $205$ ${}^\circ\mathrm{C}$ before being dropped into

Question

A metal cube is heated to a temperature of $205$ ${}^\circ\mathrm{C}$ before being dropped into a liquid. As the cube cools, its temperature, $T$ ${}^\circ\mathrm{C}$, $t$ minutes after it enters the liquid is given by $T = K + 175\mathrm{e}^{-mt}$, where $K$ and $m$ are constants. Show that the value of $K$ is $30$.[1] When $t = 3$, the temperature of the cube reaches $128$ ${}^\circ\mathrm{C}$. Find the value of $m$.[3] Find the rate at which the temperature of the cube is decreasing at the instant when $t=8$.[3] Explain why the temperature of the cube can never fall below $30^\circ$.[2]

Accepted Answer

$\boxed{-5\leq p<-4}$

2025 SST PRELIMS P1 Q3

2025 SST PRELIMS P1 Q3

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