Each student will be given a different set of data for loggerhead and green turtles. All data was collected at the end of each year indicated. Here is your data:- It is recommended that you use Graph 4.3 or a similar graphing package when completing this assignment. Make sure all graphs are suitably calibrated,labelled and titled. From your individual data regarding turtle populations, you are first required to produce a scatterplot of N against r for both turtle populations. Use one set of axes for Loggerheads and a second set of axes for Green Turtles. Use a graphing package to do this. a) Now use an algebraic approach to determine a formula for each of your two graphs. Both graphs represent exponential functions of the form N = a b'" Show full working. b) Produce a graph of your derived functions against their scatterplots. [i.e. produce two graphs, each graph showing scatterplot points and the line representing a function from part (a).1 Now use these graphs to comment on the reasonableness of your derived models. Year 1990 L99t 1992 1993 1994 1995 1996 1997 1998 1999 r (years) 0 I ) 3 4 5 6 7 8 9 Number loggerheads 662 s94 533 479 429 385 346 310 279 250 Number green turtles 918 775 6s4 552 466 394 332 281 237 200 Sunshine Coast Grammar School Year 11 Maths B Semester 2 Extended Modelling and problem Solving Task 2015 c) Scientists believe that a turtle population is at risk when turtle numbers drop below 100 animals. (i) (ii) (iii) Comment on the decline of both populations, justifying which population you believe to be most at risk and why. Determine both algebraically and graphically when your selected turtle population is likely to become 'at risk'. In Class Component Ouestion 2. (B. C standard) "Bring back the Loggers" At the end of 2000, the residents of Mon Repos volunteered to turn off their house lights facing the beach during the nesting months. Scientists believe that this will result in an increase of 17 7o for the loggerheads. a) Produce a formula modelling Loggerhead population against time for the years 2000 to 2OOg. Show full working. b) At this rate, how many years will it take before the number of loggerheads will exceed their original I 990 population? Ouestion 3. (B, C, A standard) "P,eality Check" In reality the Loggerhead population did not increase as expected in Question 2. The following data was collected regarding Loggerhead numbers from 2000 to 2009. Produce a scatterplot showing Loggerhead numbers from 2000 to 2009. On one set of axes, plot the predicted turtle numbers as indicated by your derived model in Question 2 and actual turtle numbeis as indicated in the table above. Comment in reasonable depth on similarities/differences between the scatterplots, including relevant reasoning and explanation. Use the Logistics Regression Function on your Graphics calculator to determine a model for the data supplied above. Use your calculator to check the reasonableness of your model.(\i,1{}i'1tj In 2000, when residents' lights were turned off, Green turtte JumOers were also affected. Develop a Logistics model which will model the population growth of the Green turtles if scientists believe the Mon Repos area could sustain a maximum Green turtle population of 1200 animals. You may assume that the Green turtle population reaches its maximum numbers in a similar time period as the Loggerhead population in part b).

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