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(A) According to Newton's law of cooling,the rate of cooling is proportional to the temperature difference between the body and its surroundings: $\fr

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$t_1 < t_2 < t_3$

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(A) According to Newton's law of cooling,the rate of cooling is proportional to the temperature difference between the body and its surroundings: $\frac{d heta}{dt} = k( heta_{avg} - heta_0)$.This implies that the time taken to cool by a fixed amount increases as the average temperature of the body decreases.For the three intervals:Case $1$: Average temperature $ heta_{avg1} = \frac{75+70}{2} = 72.5^{\circ} C$.Case $2$: Average temperature $ heta_{avg2} = \frac{70+65}{2} = 67.5^{\circ} C$.Case $3$: Average temperature $ heta_{avg3} = \frac{65+60}{2} = 62.5^{\circ} C$.Since $ heta_{avg1} > heta_{avg2} > heta_{avg3}$,the rate of cooling is highest in the first interval and lowest in the third interval.Therefore,the time taken $t$ is inversely proportional to the rate of cooling,leading to $t_1 < t_2 < t_3$.

$A$ bucket full of hot water is kept in a room. If it cools from $75^{\circ} C$ to $70^{\circ} C$ in $t_1$ minutes,from $70^{\circ} C$ to $65^{\circ} C$ in $t_2$ minutes and $65^{\circ} C$ to $60^{\circ} C$ in $t_3$ minutes,then

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