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Transcript
Doubling Time and Half time Doubling Time The time it takes for something to double in size t d where: Equation: 0 P – Population P P (2) P0-Initial Population t- Time d – Doubling time 2 – base for doubling Example 1 A bacterial culture began with 10 bacteria. Its growth can bet modeled using the formula B 10(2) 8 , where B is the number of bacteria after t hours. a) What is the doubling time? b) How many bacteria are present after 8 hours? c) How many bacteria are present after 16 hours? Example 1 B 10(2) t 8 a) What is the doubling time? 8 hours b) How many bacteria are present after 8 hours? 8 1 8 B 10 ( 2 ) 10 ( 2 ) 10(2) 20 Substitute t=8 There are 20 bacteria after 8 hours c) How many bacteria are present after 16 hours? How does it relate to doubling? 16 8 2 B 10 ( 2 ) 10 ( 2 ) 10(4) 40 Substitute t=16 There are 40 bacteria after 16 hours It relates to doubling because the bacteria double twice from the initial population Half Life The time it takes for a quantity to decay or be reduced to half its original amount. 1 M M0 M – Final quantity 2 Equation: M0-Initial quantity t- Time h – Half life 1/2 – base for halving t h where: Example 2 The half-life of Iodine-131 (Radioactive), is 8 days where, with an initial amount of 50g, the final t quantity can be modeled by 1 8 M 50 2 How much Iodine is left after: 8 days? 12 days? Example 2 Solutions How much Iodine is left after: 8 days? Substitute t=8 t 8 8 8 1 1 1 1 1 M 50 50 50 50 25 2 2 2 2 There’s 25g of Iodine after 8 days. 12 days? 12 8 1.5 1 1 M 50 50 2 2 500.354 17.68 There’s 17.68g of Iodine after 12 days