If initially there are 'n' bacteria, their number grows to '3n +8' after one second because of the birth of new bacteria. The number of bacteria grows in this
manner for 10 seconds. It is known that no bacterium dies in the first 10 seconds. If the number of new bacteria born in the 5th second is 8748, how many
bacteria were born in the 1st second?
Answers
Answer:
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Given : initially there are 'n' bacteria, their number grows to '3n +8'
after one second because of the birth of new bacteria.
The number of bacteria grows in this manner for 10 seconds.
It is known that no bacterium dies in the first 10 seconds.
If the number of new bacteria born in the 5th second is 8748,
To Find : how many bacteria were born in the 1st second
Solution:
Initially bacteria = n
After 1 second bacteria = 3n + 8
After 2 second bacteria = 3(3n + 8) + 8 = 9n + 32
After 3 second bacteria = 3(9n + 32) + 8 = 27n + 104
After 4 seconds bacteria = 3(27n + 104) + 8 = 81n + 320
After 5 seconds bacteria = 3(81n + 320) + 8
New bacteria born in 5th second = 3(81n + 320) + 8 - 81n + 320
= 2(81n + 320) + 8
2(81n + 320) + 8 = 8748
=> 2(81n + 320) = 8740
=> 81n + 320 = 4370
=> 81n = 4050
=> n = 50
Bacterial born in 1st second = 3n + 8 - n = 2n + 8
= 2(50) + 8
= 108
108 bacterial born in 1st second
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