The daily % increase in the population of bacteria in a colony increases by 10% points every day. On the first day, the population of bacteria increases by 20%. Find the increase in the number of bacteria on the 2nd day, if there were 1872 more bacteria at the end of the 3rd day compared to the end of the 2nd day.
Explanation:
Percentage increase in bacteria on Day 1 = 20% Day 2 = 30% Day 3 = 40% ... and so on
Let the number of bacteria at the end of Day 1 be x. ∴ Number of bacteria at the end of Day 2 = x × 1.3 = 1.3x ∴ Number of bacteria at the end of Day 2 = x × 1.3 × 1.4 = 1.82x
⇒ 1.82x - 1.3x = 1872 ⇒ 0.52x = 1872 ⇒ x = 1872/0.52 = 3600
∴ There were 3600 bacteria at the end of day 1. ⇒ Number of bacteria at the beginning of Day 1 = 3600/1.2 = 3000
Hence, 3000.
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