Exponential Population Growth Rate

... Year 12 Maths B Exponential Population Growth Rates Semester 1, 2009 Contents Task 1: 3 Forest A 3 Task 2: 7 Forest B 7 Task 3: 9 A. 9 B. 11 Task 4: 12 A. 12 B. 12 Task 1: Forest A Time(t weeks) 0 1 4 5 10 No. Of Insects (N 1000's) 372 208 168 64 Plot a graph of log N against t for the forest. Use this graph to find a model for the data in the form: N = N0bt Confirm your accuracy of your findings algebraically Use your results to complete the table above. Therefore in order to plot a graph two points need to be decided, these are the start and stop points, which are determined from the log of the first and last week: Therefore: = log10 (week 1) And = log10 (week 10) = log10 (372000) = log10 (64000) = 5.57054294 = 4.806179974 ˜ 5.5705 ˜4.8068 Therefore initial graph is represented as: To confirm the graph algebraically: N= N0bt 372000 = N0b1 & 64000 = N0b10 N0 = & N0 = = = b-9 = b9 = b = b = .8223766705 N0 = = = 452347.4624 ˜ 452347 Insects

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