2. A team of scientists began studying the population of white-tailed deer in a large wooded...

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2. A team of scientists began studying the population of white-tailed deer in a large wooded area in 2005. In 2007 (t = 2), there were 31 white-tailed deer in the wooded area. In 2020 (t = 15), there were 136 white-tailed deer. The number of white-tailed deer in the wooded area can be modeled by the function D given by D(t) = ab', where D(t) is the number of white-tailed deer during year t, and t is the number of years since 2005. (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 D(t). (ii) Find the values for a and b as a decimal approximation. (B) (i) Use the given data to find the average rate of change in the number of white-tailed deer, in deer per year, from t = 2 to t = 15 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 white-tailed deer in the wooded area for t = 19 years. Show the computations that lead to your answer. (iii) Consider the values that result from using the average rate of change found in (i) to estimate the number of white-tailed deer in the wooded area for times t = p years, where 2 2. A team of scientists began studying the population of white-tailed deer in a large wooded area in 2005. In 2007 (t = 2), there were 31 white-tailed deer in the wooded area. In 2020 (t = 15), there were 136 white-tailed deer. The number of white-tailed deer in the wooded area can be modeled by the function D given by D(t) = ab', where D(t) is the number of white-tailed deer during year t, and t is the number of years since 2005. (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 D(t). (ii) Find the values for a and b as a decimal approximation. (B) (i) Use the given data to find the average rate of change in the number of white-tailed deer, in deer per year, from t = 2 to t = 15 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 white-tailed deer in the wooded area for t = 19 years. Show the computations that lead to your answer. (iii) Consider the values that result from using the average rate of change found in (i) to estimate the number of white-tailed deer in the wooded area for times t = p years, where 2