9709 P33 - Nov 2015 - Q10
2297
Naturalists are managing a wildlife reserve to increase the number of plants of a rare species. The number of plants at time t years is denoted by N, where N is treated as a continuous variable.
(i) It is given that the rate of increase of N with respect to t is proportional to (N - 150). Write down a differential equation relating N, t and a constant of proportionality.
(ii) Initially, when t = 0, the number of plants was 650. It was noted that, at a time when there were 900 plants, the number of plants was increasing at a rate of 60 per year. Express N in terms of t.
(iii) The naturalists had a target of increasing the number of plants from 650 to 2000 within 15 years. Will this target be met?
