Consider a heat-producing electronic component (a resistor, transistor, com- puter processor, etc.) mounted to a heatsink in some electronic device (a computer, audio amplifier, suppose the device has been used heavily so that the heatsink has reached a temperature of 80 degrees celsius. (the heatsink is made of a material like aluminum that conducts heat very well, so we will assume the temperature of the heatsink is constant at all points of the heatsink.) suppose that the device is then turned off and the ambient temperature is 25 degrees celsius. according to newton's law of cooling the temperature of the heatsink will decrease over time) at a rate proportional to the difference between the temperature of the heatsink and the ambient temperature (which we assume remains constant). suppose this proportion- ality constant is 5 per minute. derive a formula for the temperature t(0) (in degrees celsius) of the heatsink t minutes after the device is turned off. what is the limit of t(t) as t approaches infinity? be sure your answer is physically reasonable!