How many time constant will elapse before the power delivrered by the battery drops to half of its maximum value.

Explanation

Power delivered by a battery is given by `P = EI. P prop I`, so if
power becomes half, current becomes half.
`I = I_0e^(-t//tau)(I_(0))/(2)=I_(0)e^(-t//tau)`or `e^(t//tau)=2` or `t = tau In 2 = 0.69tau`