An ecologist began studying a certain type of plant species in a wetlands area in 2013. In 2015 (t = 2), there were 59 plants. In 2021 (f=8), there were 118 plants. The number of plants in this species can be modeled by the function P given by P(t)= ab', where P(t) is the number of plants during year t, and f is the number of years since 2013. (A) (i) Use the given data to write two equations that can be used to find the values for constants a and b in the expression for P(t). (ii) Find the values for a and b as decimal approximations. (B) (i) Use the given data to find the average rate of change of the number of plants, in plants per year, from t=2 to t=8 years. Express your answer as a decimal approximation. Show the computations that lead to your answer. (ii) Use the average rate of change found in (i) to estimate the number of plants for t = 10 years. Show the work that leads to your answer. (iii) The average rate of change found in (i) can be used to estimate the number of plants during year t for t > 10 years. Will these estimates, found using the average rate of change, be less than or greater than the number of plants predicted by the model P during year t for t > 10 years? Explain your reasoning. (C) For which t-value, t=6 years or t=20 years, should the ecologist have more confidence in when using the model P? Give a reason for your answer in the context of the problem.