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

Answer:

Number of bacteria after 100 days is 1237.

Step-by-step explanation:

Since bacterial growth is a geometrical sequence.

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

$S_{n}=\frac{a(r^{n}-1)}{r-1}$

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

$S_{100}=\frac{1[(1.04)^{100}-1)]}{1.04-1}$

       = $\frac{(50.5049-1)}{(0.04)}$

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

Therefore, number of bacteria after 100 days is 1237.