A wildlife sanctuary monitors the number of deer (in hundreds) in its reserve. The population at time t years is represented by a differentiable function N(t) satisfying
N′(t)=90−12t,for 0≤t<10.
Answer the following questions.
(a) Part 1: (i) Find the intervals in 0≤t<10 on which the deer population is increasing and on which it is decreasing.
(b) Part 2: (ii) Explain in words what your answer in part (i) means for the sanctuary management.
(c) Part 3: (iii) Determine the year within 0≤t<10 when the population attains its maximum value, and justify your answer.