Doubling Time and Half time Doubling Time The
Doubling Time and Half time
Doubling Time The time it takes for something to double in size Equation: P – Population P 0 -Initial Population t- Time d – Doubling time 2 – base for doubling where:
Example 1 �A bacterial culture began with 10 bacteria. Its growth can be modeled using the formula , 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 8 hours a) What is the doubling time? b) How many bacteria are present after 8 hours? 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? 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. Equation: M – Final quantity M 0 -Initial quantity t- Time h – Half life 1/2 – base for halving where:
Example 2 The half-life of Iodine-131 (Radioactive), is 8 days where, with an initial amount of 50 g, the final quantity can be modeled by How much Iodine is left after: 8 days? 12 days?
Example 2 Solutions How much Iodine is left after: 8 days? Substitute t=8 There’s 25 g of Iodine after 8 days. 12 days? There’s 17. 68 g of Iodine after 12 days
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