In a bacteria culture under observation in a laboratory, the population of 50 bacteria doubles itself every hour. (1) Which of the following expressions gives the bacterial population after n hours ? 1. 2. 25n 3. 50 x 2n 4. (2) The population size of the bacteria after 3 hours will be 1. 200 2. 300 3. 400 4. 500 (3) How many bacteria will be there in the culture after 1 day ? 1. 2. 50 x 224 3. 50 x 212 4. (4) If the culture is observed after every one hour, find the number of hours after which the population size of the bacteria will be larger than 1000. 1. 5 2. 6 3. 8 4. 10

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KnowledgeBoat · Accepted Answer

(1) Given: Initial Population = 50 Growth Rate = Doubles every hour (x2) The population starts at 50 and multiplies by 2 for every hour. General formula after n hours: Population = 50 × 2n Hence, option 3 is the correct option. (2) Population size after 3 hours = ? Population size after n hours = 50 × 2n [From step 1] By replacing the value of 'n' with 3, we get: Population size after 3 hours = 50 × 23 = 50 x 8 = 400 Hence, option 3 is the correct option. (3) Bacteria in the culture after 1 day = ? We know that 1 day has 24 hours Population size after n hours = 50 × 2n [From step 1] By replacing the value of 'n' with 24, we get: Bacteria in the culture after 1 day = 50 × 224 Hence, option 2 is the correct option. (4) After how many hours will the population be larger than 1000? Let's test hours (n): n = 4: 50 x 24 = 50 x 16 = 800 n = 5: 50 x 25 = 50 x 32 = 1600 Since 1600 1000, it happens at 5 hours. Hence, option 1 is the correct option.

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