dtdT=k(TTs)Newtons law of heating/ cooling

where T is the temperature, Ts is the surrounding temperature, and k is the Heat-Transfer Coefficient which is dependent on the object's material as well as its surroundings. For this problem, the GeoGebra Slope Field Plotter is recommended.

a) Suppose you have an unknown material with a Heat-Transfer Coefficient of

k = -.05 in a room with an initial of 25 Celsius that is to be heated up to a temperature of Ts = 300 Celsius.

Record the differential equation below.

b) Derive the function from the differential equation you found in part (a) that models the temperature of the material as a function of time.

c) Using a slope field generator, describe and interpret the solution that goes through the point (20,250). For this particular solution, what was the object's initial temperature?

d) The work above is the initial condition. For this unknown material, there is an equilibrium solution that can be seen by drawing the slope field. Find, and interpret in words, this equilibrium solution. Why does the equilibrium solution make sense with the description of the problem?

Please show all the steps. I am in clac 2