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Growth

Growth. Ch 3 Lesson H. Growth. Quantities that increase exponentially (i.e. growth) Population of animals, people, bacteria etc. Biological Growth.

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Growth

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  1. Growth Ch 3 Lesson H

  2. Growth • Quantities that increase exponentially (i.e. growth) • Population of animals, people, bacteria etc.

  3. Biological Growth • Consider a population of 100 mice which under favorable conditions is increasing by 20% each week. To increase a quantity by 20%, we multiply it by 120% or 1.2. • So Pn is the population after n weeks, then P0 = 100 P1 = P0 x 1.2 = 100 x 1.2 P2 = P1 x 1.2 = 100 x (1.2)² P3 = P2 x 1.2 = 100 x (1.2)^3, etc. And from this pattern we see that Pn = 100 x (1.2)ⁿ

  4. Biological Growth • Alternately this is an example of a geometric sequence and we could have found the rule to generate it. • r = 1.2 and so as Pn = P0rⁿ then Pn = 100 x (1.2)ⁿ for n=1,2,3,….

  5. Example • An entomologist, monitoring a grasshopper plague, notices that the area affected by the grasshopper is given by An = 1000x 2^0.2n hectares, where n is the number of weeks after the initial observation. • Find the original affected area • Find the affected area after 5 weeks and 10 weeks • Find the affected area after 12 weeks • Draw the graph of An against n

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