Question

wo crafty bacteria fall into a pot of milk which has recently been sterilized. They reproduce at a rate of 4% per day. Determine how many bacteria will be present after 100 days.

Answer 1

Number of bacteria after 100 days is 1237.

Explanation:

Since bacterial growth is a geometrical sequence.

Therefore, their population after time t will be represented by the expression

`S_(n)=(a(r^(n)-1))/(r-1)`

Where a = first term of the sequence

r = common ratio of the sequence

n = duration or time

Since first term of the sequence = number of bacteria in the start = 1

Common ratio = r = (1 + 0.04) = 1.04

`S_(100)=(1[(1.04)^(100)-1)])/(1.04-1)`

=
`((50.5049-1))/((0.04))`

= 1237.64 ≈ 1237 [Since bacteria can't be in fractions]

Therefore, number of bacteria after 100 days is 1237.