Please help me with how to solve this problem and please explain step by step explanation.
Newton's law of cooling indicates that the temperature of a warm object will decrease exponentially with time and will approach the temperature of the surrounding air. The temperature T(t) is modeled by T(t) = Ta + (T0 - Ta)e-kt. In this model, Ta represents the temperature of the surrounding air, T0 represents the initial temperature of the object and t is the time after the object starts cooling. The value of k is the cooling rate and is a constant related to the physical properties of the object.

A cake comes out of the oven at 380°F and is placed on a cooling rack in a 65°F kitchen. After checking the temperature several minutes later, it is determined that the cooling rate k is 0.042. Write a function that models the temperature T(t) (in °F) of the cake t minutes after being removed from the oven.

T(t) = 380 + 65e^0.042t
T(t) = 65 + 315e^0.042t
T(t) = 65 + 380e^0.042t
T(t) = 65 + 315e^-0.042t