Differential Equations A level Pure math question

11 Naturalists are managing a wildlife reserve to increase the number of plants of a rare species, The number of plants at time / years is denoted by .. where N is treated as a continuous variable. It is given that the rale of increase of N with respect to ! is proportional to ( N -120). (a) Write down a differential equation relating N and i [1] Initially, the number of plants was 600. It is noted than at a time when there were 750 plants, the muumber of plants was increasing at a rate of h ] per year. (b) Express N in terms of /. 16: (e) The naturalist has a target of increasing the number of plants from 600 to 2500 within 15 years, Justify whether this target will be mel. 127