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Exponential growth and decay

Exponential growth and decay. Let us begin. You go on holiday and leave a particularly lovely block of cheese in the fridge. Describe what will happen to it over time?. Is the cheese decaying or is the mould growing? Mould growth can be predicted using an exponential growth model.

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Exponential growth and decay

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  1. www.mathssandpit.co.uk/blog Exponential growth and decay

  2. www.mathssandpit.co.uk/blog Let us begin • You go on holiday and leave a particularly lovely block of cheese in the fridge. • Describe what will happen to it over time?

  3. www.mathssandpit.co.uk/blog • Is the cheese decaying or is the mould growing? • Mould growth can be predicted using an exponential growth model. • The trickiest bit is extracting the information to form the model.

  4. www.mathssandpit.co.uk/blog The Growth Model How can you find A if you have P0? t represents time P0 represents the population when t = 0 P = A × e kt P represents population How can you find k if you have P1? What is happening if k is negative? A and k are constants

  5. www.mathssandpit.co.uk/blog The Growth Model: Cheese Find A The initial population of mould is 500 spores P = A × e kt 500 = A × e k × 0 500 = A × e 0 500 = A × 1 A = 500

  6. www.mathssandpit.co.uk/blog The Growth Model: Cheese The initial population of mould is 500 spores After 2 days the population is 1300 P = 500 × e kt 1300 = 500 × e k ×2 13 = 5 × e 2k 13 ÷ 5 = e 2k Find k ln (2.6) = ln (e 2k) ln (2.6) = 2k k = 0.5 ln (2.6) = 0.478 (3dp)

  7. www.mathssandpit.co.uk/blog The Growth Model: Cheese The initial population of mould is 500 spores After 2 days the population is 1300 P = 500 × e 0.478t P = 500 × e 0.478 × 14 How many spores are there by the end of the second week? P = 500 × e 6.692 P = 402966 (nearest whole number)

  8. www.mathssandpit.co.uk/blog Would you eat the cheese?

  9. www.mathssandpit.co.uk/blog Image credits https://crowarrowinc.wordpress.com www.thegrocer.co.uk Microsoft clipart www.basenow.net

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