In a chemical reactor, the instantaneous rate of heat generation (in kilowatts) during the first ten minutes of operation is modeled by
q(t)=pe−0.2t+4,0≤t≤10,
where t is measured in minutes and p is a positive constant that can be adjusted by the engineer.
The engineer requires that the average rate of heat generation over the interval [0,10] be exactly 5 kW.
Respond to the following prompts.
(1) Determine the value of p that meets the engineer’s requirement. Round your answer to the nearest tenth.
(2) Interpret the numerical value found in part (a) in the context of the reactor’s operation. Explain what the constant p represents physically and how its value affects the heat-generation profile.