The dynamics of a population, with its growth characterised by two stages namely an initial non-reproductive stage of length ρ, resistant to the environmental fluctuations and a second susceptible stage adding continuously to the population is modelled. The environment alternates in its character being hostile and favourable.The favourable periods are independently and identically distributed random variables and during the constantharsh periods all the adults in the population are wiped out While the existing models tacitly assume the environmental period to be much smaller than the biological period ρ, our modelling enables us to consider the two periods to be of comparable scale. In such a case, apart from the various statistical characteristics of interest derived, we show that the average extinction time increases with increasing duration of the disturbance, a result which is counter-intutive.Numerical evaluation of the time for extinction for certain values of the parameters involved are made.