A group of scientists studying the population of small marsupials used N to stand for the

number of animals in the population and t for the number of months since they began

the study, with the entire study lasting for 2 years. They determined that the population

during this time could be accurately modelled by the function

N(t) = 50 - 4t + 0.2t².

a) Calculate N (0) and N(2). Give a possible interpretation of these values.

b) Calculate N(-1) and N(30). Are these values appropriate for this model?

c) According to this model, at what time(s) are there exactly 50 marsupials?

d) In what other ways could the scientists have chosen to represent this function?

e) The scientists identified this function by writing N = N(t). What did this mean?