10 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.
- 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.
- 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 \(t\).
- The naturalists had a target of increasing the number of plants from 650 to 2000 within 15 years. Will this target be met?