Answer
22.5 J is absorbed
Work Step by Step
Here, passive reference configuration is not followed, so power = -vi = -(-15)3$e^{-2t}$ = 45$e^{-2t}$ W, is always positive. This implies energy is delivered to the element.
E = $\int P dt $
Energy transferred from t = 0 to t = $\infty$
= $$\int_{0}^{\infty} P dt$$ = $$\int_{0}^{\infty} 45e^{-2t} dt$$ = 22.5 J
