QUESTION $4[25$ MARKS$]$

You have a freshly baked Cromboloni that has just been taken out $of$ the oven. The cooling rate

$of$ the Cromboloni $is$ directly proportional $to$ the difference between its temperature and the

surrounding temperature, $25C.$ This situation can $be$ described using Newton's Law $of$

Cooling, given $by$ the equation:

$\frac{dT}{dt}=-k(T-25)$

where:

$tis$ the time $(min).$

$TCkis$ cooling constant $(per$ min$).$

Suppose the initial temperature $of$ the Cromboloni $is120C,$ and the $kis0\mathrm{.}16$ per minute.

Calculate $to$ the most accurate value $of$ the time, $t$ takes for the Cromboloni $to$ cool down $to$

$27C.$