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160.104 Introductory mathematics for Science

Find the population size on Triangle Island for your model after 1, 2, 3, 4 and 5generations by setting up a table like the one below in your spreadsheet. Enter yourspreadsheet formula forNinto the first cell and then use autofill to find the remainingpopulation sizes.t012345N3.Add a row to your table and use it to find the logarithm of eachNin Question 2.logN4.In your spreadsheet, create 2 separate graphs (on separate axes), making sure in eachone the axes are clearly numbered and labelled:(a)N against.t(b)logN against.t5.One of your two graphs in Question 4, should be a straight line.(a)Using two points on the line and a formula in your spreadsheet, find the gradient ofthis line.(b)By inspecting the graph, find the vertical intercept of this line.(c)Use logs to show why this graph produced a straight line, and how you could havepredicted your values for the gradient and vertical intercept. [You are typing thiswork into the spreadsheet.]6.The multiplicative rate? in your population formula, is determined by the birth rateBand the death rateD of the population:??1.BD???? Using your values from thestart, the death rateD of your population is your value forc.Using your values for? andD, use algebra to determine your population’s birth rate.B [You are typing this work into the spreadsheet.]7.Not far away from Triangle Island is Square Island. The birth rate on Square Island is halfof the birth rate on Triangle Island, but the death rate is the same.Based on your values, find(a)the multiplicative rate for population growth on Square Island(b)the formula for the Square Island population growth model.8 – 11. Repeat questions 2 – 5 for your population on Square Island.12. Discuss the changes made to your straight line by halving the birthrate. (What is thesame? What is different?)

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