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Exponential Functions Field Biologist Katie wishes to reintroduce gray wolves in New Mexico. She has collected a strong healthy male and 2 strong healthy females. She needs to predict how many wolves there will be in 40 years. She also wants to know in what year (if ever) there will be 2000 wolves if she releases them in 2014. You will help her solve these problems by doing the following: Start with 3 die. Each die represents a wolf and each throw represents one year. A roll of 3 or 6 represents the birth of a pup, so each time one of these numbers comes up, add a die to the population. If a 1 comes up, a death has occurred, so remove one die from the population. Continue the process until you do not have enough die to complete another trial. Record the data in a table similar to the one below. Trial number (years Population since 2014) 0 3 1 2 a. b. Enter the trial numbers in List 1 and the population into List 2 in your calculator. Make a scatter plot. Looking at the pattern of the points what model do you think would best fit the data? Why? Find the common ratio for each pair of points. Call it ‘b’. Now average all your ‘b’ values to get a representation of the experiment. This is your growth factor. c. What is your growth rate? ( Hint: b = 1+growth rate) d. Write an exponential function that would best model this data, then graph it over your scatter plot. Do you think it is a good fit? e. Using the equation as your mathematical model, what do you predict the wolf population to be after 40 years? f. Will there ever be a wolf population greater than 2000? And if so what year should this occur? Is this reasonable? Justify your answer.