Question: During a surge in the demand for electricity, the rate, r, at which energy is used can be approximated by r = te at ,

During a surge in the demand for electricity, the rate, r, at which energy is used can be approximated by

r = te^−at,

where t is the time in hours and a is a positive constant.
(a) Find the total energy, E, used in the first T hours. Give your answer as a function of a.
(b) What happens to E as T → ∞?

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