The circuit below is used to heat water kept in a bucket. Assuming...

In given condition,

Heat gained by water heater $-$ Heat lost governed by Newton's law of cooling = Net heat gained by water 

$⇒ {i}^{2}{R}_{1} - K\left(T - {T}_{0}\right) = mS\left(\dfrac{\DeltaT}{\Deltat}\right)$

Here, $T =$ temperature and $t =$ time.

$⇒ \dfrac{dT}{dt} = \dfrac{{i}^{2}{R}_{1}}{mS} - \dfrac{K}{mS}\left(T - {T}_{0}\right)$

$= \dfrac{{i}^{2}{R}_{1}}{mS} + \dfrac{K{T}_{0}}{mS} - \dfrac{K}{mS}T$

Above equation can be written as, 

$\dfrac{dT}{dt} = A + BT$

or $\dfrac{dT}{A + BT} = dt$

Integrating, we get 

$⇒ \dfrac{1}{B} . \log_{e}\left(A + BT\right) = t$

$⇒ A + BT = {e}^{tB}$

$⇒ T = \dfrac{1}{B}\left({e}^{tB} - A\right)$

Hence, temperature $T$ depends on time $t$ exponentially.

$∴$ Best suitable graph is