Answer: [tex]\dfrac{dT(t)}{dt}=77\times (450-T)[/tex]
Step-by-step explanation:
Given
The temperature of the liquid is [tex]75^{\circ}F[/tex] placed in an oven with temperature of [tex]450^{\circ}F[/tex].
Initially difference in temperature of the two
[tex]\Delta T=450-75\\\Rightarrow \Delta T=375^{\circ}F[/tex]
According to the question
[tex]\Rightarrow \dfrac{dT(t)}{dt}=77\cdot \Delta T\\\\\Rightarrow \dfrac{dT(t)}{dt}=77\times (450-T)\quad [\text{T=75}^{\circ}F\ \text{at t=0}][/tex]
