Ere is considerable evidence to support the theory that for some species there is a minimum population TT, called the critical threshold, such that a species will become extinct if the size of the population falls below TT. This condition can be incorporated by introducing the factor −(1−P/T)−(1−P/T) into the logistic equation. Thus, the modified logistic model is given by the differential equation: dPdt=−rP(1−PK)(1−PT)dPdt=−rP(1−PK)( 1−PT), P, t≥0P, t≥0. Suppose that for some species the intrinsic growth rate is r=0.004r=0.004, the environmental carrying capacity is K=23000K=23000 and the critical threshold is T=900T=900. For what values of PP is the population increasing and decreasing? Write your answers in interval notation. If there is more than one interval, use capital U for union.