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Question

Mathematics Question on Compound Interest

In a laboratory, the count of bacteria in a certain experiment was increasing at the rate of 2.52.5 % per hour. Find the bacteria at the end of 22 hours if the count was initially 5,06,0005,06,000.

Answer

The initial count of bacteria is given as 5,06,0005,06,000.
Bacteria at the end of 22 hours = 506000(1+2.5100)2506000\bigg(1+\frac{2.5}{100}\bigg)^2

= 506000(1+140)2=5060000×4140×4140506000\bigg(1+\frac{1}{40}\bigg)^2 = 5060000 × \frac{41}{40} × \frac{41}{40}
531616.25=5,31,616  (approx)531616.25 = 5,31,616 \;(approx)

Thus, the count of bacteria at the end of 22 hours will be 5,31,616  (approx.)5,31,616 \;(approx.).